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Автор: Grafiati

Опубліковано: 8 червня 2024

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1

YANG, QILIN. "(k, s)-POSITIVITY AND VANISHING THEOREMS FOR COMPACT KÄHLER MANIFOLDS." International Journal of Mathematics 22, no. 04 (April 2011): 545–76. http://dx.doi.org/10.1142/s0129167x11006908.

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We study the (k, s)-positivity for holomorphic vector bundles on compact complex manifolds. (0, s)-positivity is exactly the Demailly s-positivity and a (k, 1)-positive line bundle is just a k-positive line bundle in the sense of Sommese. In this way we get a unified theory for all kinds of positivities used for semipositive vector bundles. Several new vanishing theorems for (k, s)-positive vector bundles are proved and the vanishing theorems for k-ample vector bundles on projective algebraic manifolds are generalized to k-positive vector bundles on compact Kähler manifolds.

2

Ein, Lawrence, Oliver Küchle, and Robert Lazarsfeld. "Local positivity of ample line bundles." Journal of Differential Geometry 42, no. 2 (1995): 193–219. http://dx.doi.org/10.4310/jdg/1214457231.

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3

Szemberg, Tomasz. "On positivity of line bundles on Enriques surfaces." Transactions of the American Mathematical Society 353, no. 12 (July 30, 2001): 4963–72. http://dx.doi.org/10.1090/s0002-9947-01-02788-x.

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4

Küronya, Alex, and Victor Lozovanu. "Positivity of Line Bundles and Newton-Okounkov Bodies." Documenta Mathematica 22 (2017): 1285–302. http://dx.doi.org/10.4171/dm/596.

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5

Biswas, Indranil, Krishna Hanumanthu, and D. S. Nagaraj. "Positivity of vector bundles on homogeneous varieties." International Journal of Mathematics 31, no. 12 (September 24, 2020): 2050097. http://dx.doi.org/10.1142/s0129167x20500974.

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We study the following question: Given a vector bundle on a projective variety [Formula: see text] such that the restriction of [Formula: see text] to every closed curve [Formula: see text] is ample, under what conditions [Formula: see text] is ample? We first consider the case of an abelian variety [Formula: see text]. If [Formula: see text] is a line bundle on [Formula: see text], then we answer the question in the affirmative. When [Formula: see text] is of higher rank, we show that the answer is affirmative under some conditions on [Formula: see text]. We then study the case of [Formula: see text], where [Formula: see text] is a reductive complex affine algebraic group, and [Formula: see text] is a parabolic subgroup of [Formula: see text]. In this case, we show that the answer to our question is affirmative if [Formula: see text] is [Formula: see text]-equivariant, where [Formula: see text] is a fixed maximal torus. Finally, we compute the Seshadri constant for such vector bundles defined on [Formula: see text].

6

Varolin, Dror. "A Takayama-type extension theorem." Compositio Mathematica 144, no. 2 (March 2008): 522–40. http://dx.doi.org/10.1112/s0010437x07002989.

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AbstractWe prove a theorem on the extension of holomorphic sections of powers of adjoint bundles from submanifolds of complex codimension 1 having non-trivial normal bundle. The first such result, due to Takayama, considers the case where the canonical bundle is twisted by a line bundle that is a sum of a big and nef line bundle and a $\mathbb {Q}$-divisor that has Kawamata log terminal singularities on the submanifold from which extension occurs. In this paper we weaken the positivity assumptions on the twisting line bundle to what we believe to be the minimal positivity hypotheses. The main new idea is an L2 extension theorem of Ohsawa–Takegoshi type, in which twisted canonical sections are extended from submanifolds with non-trivial normal bundle.

7

Hanumanthu, Krishna. "Positivity of line bundles on special blow ups ofP2." Journal of Pure and Applied Algebra 221, no. 9 (September 2017): 2372–82. http://dx.doi.org/10.1016/j.jpaa.2016.12.038.

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8

Hanumanthu, Krishna. "Positivity of line bundles on general blow ups of P2." Journal of Algebra 461 (September 2016): 65–86. http://dx.doi.org/10.1016/j.jalgebra.2016.04.029.

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9

Lee, Sanghyeon, and Jaesun Shin. "Positivity of line bundles on general blow-ups of abelian surfaces." Journal of Algebra 524 (April 2019): 59–78. http://dx.doi.org/10.1016/j.jalgebra.2018.12.020.

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10

Lundman, Anders. "Local positivity of line bundles on smooth toric varieties and Cayley polytopes." Journal of Symbolic Computation 74 (May 2016): 109–24. http://dx.doi.org/10.1016/j.jsc.2015.05.007.

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11

Grieve, Nathan. "Index conditions and cup-product maps on Abelian varieties." International Journal of Mathematics 25, no. 04 (April 2014): 1450036. http://dx.doi.org/10.1142/s0129167x14500360.

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We study questions surrounding cup-product maps which arise from pairs of non-degenerate line bundles on an abelian variety. Important to our work is Mumford's index theorem which we use to prove that non-degenerate line bundles exhibit positivity analogous to that of ample line bundles. As an application we determine the asymptotic behavior of families of cup-product maps and prove that vector bundles associated to these families are asymptotically globally generated. To illustrate our results we provide several examples. For instance, we construct families of cup-product problems which result in a zero map on a one-dimensional locus. We also prove that the hypothesis of our results can be satisfied, in all possible instances, by a particular class of simple abelian varieties. Finally, we discuss the extent to which Mumford's theta groups are applicable in our more general setting.

12

Park, Jinhyung. "Asymptotic vanishing of syzygies of algebraic varieties." Communications of the American Mathematical Society 2, no. 3 (June 6, 2022): 133–48. http://dx.doi.org/10.1090/cams/7.

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The purpose of this paper is to prove Ein–Lazarsfeld’s conjecture on asymptotic vanishing of syzygies of algebraic varieties. This result, together with Ein–Lazarsfeld’s asymptotic nonvanishing theorem, describes the overall picture of asymptotic behaviors of the minimal free resolutions of the graded section rings of line bundles on a projective variety as the positivity of the line bundles grows. Previously, Raicu reduced the problem to the case of products of three projective spaces, and we resolve this case here.

13

Gubler, Walter, and Klaus Künnemann. "Positivity properties of metrics and delta-forms." Journal für die reine und angewandte Mathematik (Crelles Journal) 2019, no. 752 (July 1, 2019): 141–77. http://dx.doi.org/10.1515/crelle-2016-0060.

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Abstract In previous work, we have introduced δ-forms on the Berkovich analytification of an algebraic variety in order to study smooth or formal metrics via their associated Chern δ-forms. In this paper, we investigate positivity properties of δ-forms and δ-currents. This leads to various plurisubharmonicity notions for continuous metrics on line bundles. In the case of a formal metric, we show that many of these positivity notions are equivalent to Zhang’s semipositivity. For piecewise smooth metrics, we prove that plurisubharmonicity can be tested on tropical charts in terms of convex geometry. We apply this to smooth metrics, to canonical metrics on abelian varieties and to toric metrics on toric varieties.

14

ANDREATTA, MARCO. "MINIMAL MODEL PROGRAM WITH SCALING AND ADJUNCTION THEORY." International Journal of Mathematics 24, no. 02 (February 2013): 1350007. http://dx.doi.org/10.1142/s0129167x13500079.

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Let (X, L) be a quasi-polarized pair, i.e. X is a normal complex projective variety and L is a nef and big line bundle on it. We study, up to birational equivalence, the positivity (nefness) of the adjoint bundles KX + rL for high rational numbers r. For this we run a Minimal Model Program with scaling relative to the divisor KX + rL. We give then some applications, namely the classification up to birational equivalence of quasi-polarized pairs with sectional genus 0, 1 and of embedded projective varieties X ⊂ ℙN with degree smaller than 2 codim ℙN(X) + 2.

15

Koike, Takayuki. "Plurisubharmonic functions on a neighborhood of a torus leaf of a certain class of foliations." Forum Mathematicum 31, no. 6 (November 1, 2019): 1457–66. http://dx.doi.org/10.1515/forum-2018-0228.

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AbstractLet C be a smooth elliptic curve embedded in a smooth complex surface X such that C is a leaf of a suitable holomorphic foliation of X. We investigate the complex analytic properties of a neighborhood of C under some assumptions on the complex dynamical properties of the holonomy function. As an application, we give an example of {(C,X)} in which the line bundle {[C]} is formally flat along C, however it does not admit a {C^{\infty}} Hermitian metric with semi-positive curvature. We also exhibit a family of embeddings of a fixed elliptic curve for which the positivity of normal bundles does not behave in a simple way.

16

Xu and Zhuang. "On positivity of the CM line bundle on K-moduli spaces." Annals of Mathematics 192, no. 3 (2020): 1005. http://dx.doi.org/10.4007/annals.2020.192.3.7.

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17

Grimm, Eckhard, Merle Peters, Julian Kaltenbach, Chu Zhang, and Moritz Knoche. "Growth strains cause vascular browning and cavities in ´Nicoter´ apples." PLOS ONE 18, no. 7 (July 20, 2023): e0289013. http://dx.doi.org/10.1371/journal.pone.0289013.

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‘Nicoter’ apples (Malus × domestica Borkh.) occasionally develop a disorder referred to as vascular browning. Symptomatic fruit are perceived as being of low quality. The objective was to identify the mechanistic basis of this disorder. The frequency of symptomatic ‘Nicoter’ apples differed between growing sites and increased with delayed harvest. Typical symptoms are tissue browning and cavities in the ray parenchyma of the calyx region, and occasionally also of the stem end. Cavity size is positively correlated with the extent of tissue browning. Cavities were oriented radially in the direction of the bisecting line between the radii connecting the calyx/pedicel axis to the sepal and petal bundles. Microscopy revealed cell wall fragments in the cavities indicating physical rupture of cell walls. Immunolabelling of cell wall epitopes offered no evidence for separation of cells along cell walls. The growth pattern in ‘Nicoter’ is similar to that in its parents ‘Gala’ and ‘Braeburn’. Allometric analyses revealed no differences in growth in fruit length among the three cultivars. However, the allometric analyses of growth in diameter revealed a marked increase in the distance between the surface of the calyx cavity and the vascular bundle in ‘Nicoter’, that was absent in ‘Braeburn’ and ‘Gala’. This increase displaced the petal bundles in the ray parenchyma outwards and subjected the tissue between the petal and sepal bundles to tangential strain. Rupture of cells results in tissue browning and cavity formation. A timely harvest is a practicable countermeasure for decreasing the incidence of vascular browning.

18

Popovici, Dan. "L2 Extension for jets of holomorphic sections of a Hermitian line Bundle." Nagoya Mathematical Journal 180 (2005): 1–34. http://dx.doi.org/10.1017/s0027763000009168.

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AbstractLet (X, ω) be a weakly pseudoconvex Kähler manifold, Y ⊂ X a closed submanifold defined by some holomorphic section of a vector bundle over X, and L a Hermitian line bundle satisfying certain positivity conditions. We prove that for any integer k > 0, any section of the jet sheaf which satisfies a certain L2 condition, can be extended into a global holomorphic section of L over X whose L2 growth on an arbitrary compact subset of X is under control. In particular, if Y is merely a point, this gives the existence of a global holomorphic function with an L2 norm under control and with prescribed values for all its derivatives up to order k at that point. This result generalizes the L2 extension theorems of Ohsawa-Takegoshi and of Manivel to the case of jets of sections of a line bundle. A technical difficulty is to achieve uniformity in the constant appearing in the final estimate. To this end, we make use of the exponential map and of a Rauch-type comparison theorem for complete Riemannian manifolds.

19

Campana, Frédéric, and Mihai Păun. "Positivity properties of the bundle of logarithmic tensors on compact Kähler manifolds." Compositio Mathematica 152, no. 11 (September 21, 2016): 2350–70. http://dx.doi.org/10.1112/s0010437x16007442.

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Let $X$ be a compact Kähler manifold, endowed with an effective reduced divisor $B=\sum Y_{k}$ having simple normal crossing support. We consider a closed form of $(1,1)$-type $\unicode[STIX]{x1D6FC}$ on $X$ whose corresponding class $\{\unicode[STIX]{x1D6FC}\}$ is nef, such that the class $c_{1}(K_{X}+B)+\{\unicode[STIX]{x1D6FC}\}\in H^{1,1}(X,\mathbb{R})$ is pseudo-effective. A particular case of the first result we establish in this short note states the following. Let $m$ be a positive integer, and let $L$ be a line bundle on $X$, such that there exists a generically injective morphism $L\rightarrow \bigotimes ^{m}T_{X}^{\star }\langle B\rangle$, where we denote by $T_{X}^{\star }\langle B\rangle$ the logarithmic cotangent bundle associated to the pair $(X,B)$. Then for any Kähler class $\{\unicode[STIX]{x1D714}\}$ on $X$, we have the inequality $$\begin{eqnarray}\displaystyle \int _{X}c_{1}(L)\wedge \{\unicode[STIX]{x1D714}\}^{n-1}\leqslant m\int _{X}(c_{1}(K_{X}+B)+\{\unicode[STIX]{x1D6FC}\})\wedge \{\unicode[STIX]{x1D714}\}^{n-1}.\end{eqnarray}$$ If $X$ is projective, then this result gives a generalization of a criterion due to Y. Miyaoka, concerning the generic semi-positivity: under the hypothesis above, let $Q$ be the quotient of $\bigotimes ^{m}T_{X}^{\star }\langle B\rangle$ by $L$. Then its degree on a generic complete intersection curve $C\subset X$ is bounded from below by $$\begin{eqnarray}\displaystyle \biggl(\frac{n^{m}-1}{n-1}-m\biggr)\int _{C}(c_{1}(K_{X}+B)+\{\unicode[STIX]{x1D6FC}\})-\frac{n^{m}-1}{n-1}\int _{C}\unicode[STIX]{x1D6FC}.\end{eqnarray}$$ As a consequence, we obtain a new proof of one of the main results of our previous work [F. Campana and M. Păun, Orbifold generic semi-positivity: an application to families of canonically polarized manifolds, Ann. Inst. Fourier (Grenoble) 65 (2015), 835–861].

20

Andersson, Mats. "A generalized Poincaré-Lelong formula." MATHEMATICA SCANDINAVICA 101, no. 2 (December 1, 2007): 195. http://dx.doi.org/10.7146/math.scand.a-15040.

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We prove a generalization of the classical Poincaré-Lelong formula. Given a holomorphic section $f$, with zero set $Z$, of a Hermitian vector bundle $E\to X$, let $S$ be the line bundle over $X\setminus Z$ spanned by $f$ and let $Q=E/S$. Then the Chern form $c(D_Q)$ is locally integrable and closed in $X$ and there is a current $W$ such that ${dd}^cW=c(D_E)-c(D_Q)-M,$ where $M$ is a current with support on $Z$. In particular, the top Bott-Chern class is represented by a current with support on $Z$. We discuss positivity of these currents, and we also reveal a close relation with principal value and residue currents of Cauchy-Fantappiè-Leray type.

21

Filotico, Marcello, and Alessandro D’Amuri. "Polypoid Carcinoma of the Oropharynx with Stromal Ossifying Myofibroblastic Proliferation: A Case Report and Literature Review." Case Reports in Pathology 2016 (2016): 1–7. http://dx.doi.org/10.1155/2016/2540407.

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A 76-year-old man reported a worsening difficulty in swallowing, leading to the inability to eat. Physical examination and CT scan revealed a polypoid mass on the posterior oropharynx and obstructing the oropharyngeal space. Histologically, the surface was ulcerated. In the underlying necrotic rim, there was active granulation tissue, and a proliferation of voluminous, globoid elements with hyperchromatic and irregular nucleus, sometimes arranged in a alveolar aggregate. The core of the lesion contained spindle-like myoid elements in interwoven bundles, with trabeculae of osteoid matrix maturing into calcified bone. Immunohistochemistry documented positivity for cytokeratins, epithelial membrane antigen, and P63 in the globoid elements beneath the necrotic rim; strong and diffuse expression of vimentin, smooth muscle actin, and CD99 and BCL2 in the spindle elements; and complete negativity for cytokeratin 5/6, high molecular weight cytokeratin (clone 34βE12), S100, muscle-specific actin, desmin, CD117, and anaplastic lymphoma kinase. The lesion was morphologically and immunophenotypically classified as a polypoid oropharyngeal carcinoma with ossifying myofibroblastic stromal proliferation.

22

Qiu, Hui Y., Yong Q. Xue, Jin L. Pan, Ya F. Wu, Yong Wang, Juan Shen та Jun Zhang. "A Novel Translocation (4;12)(q11;q13) in an Acute Promyelocytic Leukemia-Like Case Lacking RARα Rearrangements." Blood 108, № 11 (16 листопада 2006): 4279. http://dx.doi.org/10.1182/blood.v108.11.4279.4279.

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Abstract We report a novel chromosomal translocation t(4;12)(q11;q13) in a 37-year-old male with acute promyelocytic leukemia (APL)-like morphologic changes but lacking RARα rearrangements. His blast cells had some morphologic features evocative APL such as heavy azurophilic granules, bundles of Auer rods except regular round or oval nuclei. Immunophenotype of blast cells showed positivity for CD13 and CD33, and negativity for CD34 and HLA-DR which were compatible with the diagnosis of APL. Disseminated intravascular coagulation (DIC) was present. Chromosome study of BM cells showed that 29 out of 35 metaphases had a consistent karyotype of 46, XY, t (4;12)(q11;q13) which was confirmed by chromosome painting with whole chromosome paint probes 4 and 12. However, fluorescence in site hybridization, reverse transcriptase-polymerase chain reaction (RT-PCR) and multiplex RT-PCR did not demonstrate any evidence for RARα rearrangements including PML-RARα, PLZF-RARα, NuMA-RARα, NPM-RARαand STAT5b-RARα fusion genes. Sequential treatment with arsenic trioxide and chemotherapy had no effect, he died of bleeding due to DIC. In view of the fact as mentioned above, this case should be rated as transitional M2–M3.

23

Jabbusch, Kelly. "Positivity of cotangent bundles." Michigan Mathematical Journal 58, no. 3 (December 2009): 723–44. http://dx.doi.org/10.1307/mmj/1260475697.

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24

Hering, Milena, Mircea Mustaţă, and Sam Payne. "Positivity properties of toric vector bundles." Annales de l’institut Fourier 60, no. 2 (2010): 607–40. http://dx.doi.org/10.5802/aif.2534.

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25

Sandhu, A. D., and Y. Liu. "Endobronchial Mucus Gland Adenoma: A Case Report." American Journal of Clinical Pathology 154, Supplement_1 (October 2020): S45. http://dx.doi.org/10.1093/ajcp/aqaa161.096.

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Abstract Introduction/Objective Mucus Gland Adenoma (MGA) is a rare benign epithelial tumor with few case reports. They arise from submucosal glands and ducts of large proximal airways, but have been reported peripherally and within lung parenchyma. MGAs form an exophytic mass that causes obstructive symptoms, occurring in all ages without gender predilection. MGAs have low to no malignant potential, but may be confused with more aggressive entities. Thus, MGA may present a diagnostic challenge on frozen section. Methods We present the case of a 66-year-old male with recurrent right pneumonia and empyema. Bronchoscopy revealed an obstructing mass in the right bronchus intermedius. Biopsies and cytology were insufficient showing only benign bronchial epithelium. Therefore, the patient underwent surgical sleeve resection of the right bronchus intermedius for diagnosis and treatment. It was received in two pieces measuring 1.0 x 0.6 x 0.5 and 2.0 x 1.5 x 0.9 cm - a well-circumscribed, firm white nodule with a smooth exterior and pushing borders. Cut surfaces were mucoid, homogenous and rubbery, with cysts measuring up to 2 mm. Histology showed crowded mucus-filled acini and tubules lined by bland cuboidal to columnar cells without atypia or mitosis. The stroma showed smooth muscle bundles and lymphocytic infiltrate. Benign bronchial epithelium lined the surface. A preliminary diagnosis of “adenoma” was made, with final classification pending permanent section. Results It showed positivity for s100, CK5/6, and CAM5.2. DOG1 showed a luminal staining pattern. NapsinA was negative and TTF-1 was patchy. P63, P40, CK5/6 and calponin highlighted myoepithelial cells, underlining the benign nature of the process. Conclusion MGA may resemble adenocarcinoma, low-grade mucoepidermoid carcinoma, and other benign adenomas. It presents a diagnostic challenge on frozen section as its malignant differentials are more common. Thus, it is important to recognize and be aware of these rare, benign tumors.

26

Bartocci, Claudio, and Ugo Bruzzo. "Super line bundles." Letters in Mathematical Physics 17, no. 4 (May 1989): 263–74. http://dx.doi.org/10.1007/bf00399749.

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27

Schumacher, Georg. "Positivity of relative canonical bundles and applications." Inventiones mathematicae 190, no. 1 (January 14, 2012): 1–56. http://dx.doi.org/10.1007/s00222-012-0374-7.

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28

Lübke, Martin. "A note on positivity of Einstein bundles." Indagationes Mathematicae 2, no. 3 (September 1991): 311–18. http://dx.doi.org/10.1016/0019-3577(91)90019-4.

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29

Li, Zhi, and Xiangyu Zhou. "On the positivity of direct image bundles." Известия Российской академии наук. Серия математическая 87, no. 5 (2023): 140–63. http://dx.doi.org/10.4213/im9336.

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In the present paper, we obtain an equivalent relation between the log-plurisubharmonicity of the relative Bergman kernel, the Griffiths and Nakano positivity for the direct image with the natural $L^2$ metric, by finding a converse of Berndtsson's theorem on the direct image. A converse of Berndtsson's generalization of Kiselman minimal principle is also obtained. Bibliography: 30 titles.

30

Li, Zhi, and Xiangyu Zhou. "On the positivity of direct image bundles." Izvestiya: Mathematics 87, no. 5 (2023): 987–1010. http://dx.doi.org/10.4213/im9336e.

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In the present paper, we obtain an equivalent relation between the log-plurisubharmonicity of the relative Bergman kernel, the Griffiths and Nakano positivity for the direct image with the natural $L^2$ metric, by finding a converse of Berndtsson's theorem on the direct image. A converse of Berndtsson's generalization of Kiselman minimal principle is also obtained.

31

Deng, Fusheng, Zhiwei Wang, Liyou Zhang, and Xiangyu Zhou. "New characterization of plurisubharmonic functions and positivity of direct image sheaves." American Journal of Mathematics 146, no. 3 (June 2024): 751–68. http://dx.doi.org/10.1353/ajm.2024.a928324.

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abstract: We discover a new characterization of plurisubharmonic functions in terms of $L^p$ extension from one point and Griffiths positivity of holomorphic vector bundles with singular Finsler metrics in terms of $L^p$ extensions. As applications, we give a stronger result or new proof of some well-known theorems on the Griffiths positivity of the holomorphic vector bundles and their direct image sheaves associated to certain holomorphic fibrations.

32

Hirschowitz, A., and M. S. Narasimhan. "Vector bundles as direct images of line bundles." Proceedings Mathematical Sciences 104, no. 1 (February 1994): 191–200. http://dx.doi.org/10.1007/bf02830882.

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33

Keeler, Dennis. "Arithmetically Nef Line Bundles." Michigan Mathematical Journal 69, no. 3 (August 2020): 545–58. http://dx.doi.org/10.1307/mmj/1596700818.

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34

Brown, Morgan V. "Bigq-ample line bundles." Compositio Mathematica 148, no. 3 (March 19, 2012): 790–98. http://dx.doi.org/10.1112/s0010437x11007457.

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AbstractA recent paper of Totaro developed a theory ofq-ample bundles in characteristic 0. Specifically, a line bundleLonXisq-ample if for every coherent sheaf ℱ onX, there exists an integerm0such thatm≥m0impliesHi(X,ℱ⊗𝒪(mL))=0 fori>q. We show that a line bundleLon a complex projective schemeXisq-ample if and only if the restriction ofLto its augmented base locus isq-ample. In particular, whenXis a variety andLis big but fails to beq-ample, then there exists a codimension-one subschemeDofXsuch that the restriction ofLtoDis notq-ample.

35

ARNAUD, CELIA. "FIBER BUNDLES LINE UP." Chemical & Engineering News 88, no. 25 (June 21, 2010): 7. http://dx.doi.org/10.1021/cen-v088n025.p007.

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36

Kikuta, Shin. "Carathéodory measure hyperbolicity and positivity of canonical bundles." Proceedings of the American Mathematical Society 139, no. 04 (April 1, 2011): 1411. http://dx.doi.org/10.1090/s0002-9939-2010-10564-6.

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Liu, Kefeng, Xiaofeng Sun, and Xiaokui Yang. "Positivity and vanishing theorems for ample vector bundles." Journal of Algebraic Geometry 22, no. 2 (August 9, 2012): 303–31. http://dx.doi.org/10.1090/s1056-3911-2012-00588-8.

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38

Bauer, Thomas, Sándor J. Kovács, Alex Küronya, Ernesto C. Mistretta, Tomasz Szemberg, and Stefano Urbinati. "On positivity and base loci of vector bundles." European Journal of Mathematics 1, no. 2 (March 31, 2015): 229–49. http://dx.doi.org/10.1007/s40879-015-0038-4.

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39

Berndtsson, Bo. "Strict and nonstrict positivity of direct image bundles." Mathematische Zeitschrift 269, no. 3-4 (October 6, 2010): 1201–18. http://dx.doi.org/10.1007/s00209-010-0783-5.

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40

Yuan, Xinyi. "On volumes of arithmetic line bundles." Compositio Mathematica 145, no. 6 (November 2009): 1447–64. http://dx.doi.org/10.1112/s0010437x0900428x.

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AbstractWe show an arithmetic generalization of the recent work of Lazarsfeld–Mustaţǎ which uses Okounkov bodies to study linear series of line bundles. As applications, we derive a log-concavity inequality on volumes of arithmetic line bundles and an arithmetic Fujita approximation theorem for big line bundles.

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Schumacher, Georg. "Erratum to: Positivity of relative canonical bundles and applications." Inventiones mathematicae 192, no. 1 (February 23, 2013): 253–55. http://dx.doi.org/10.1007/s00222-013-0458-z.

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42

Chen, Huayi. "Algebraicity of formal varieties and positivity of vector bundles." Mathematische Annalen 354, no. 1 (October 16, 2011): 171–92. http://dx.doi.org/10.1007/s00208-011-0731-7.

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43

Taub, A. H. "Positivity of energy in Abelian principal bundles over spacetime." Letters in Mathematical Physics 13, no. 3 (April 1987): 201–10. http://dx.doi.org/10.1007/bf00423447.

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Braverman, Alexander, Michael Finkelberg, and Hiraku Nakajima. "Line bundles over Coulomb branches." Advances in Theoretical and Mathematical Physics 25, no. 4 (2021): 957–93. http://dx.doi.org/10.4310/atmp.2021.v25.n4.a2.

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45

Blumenhagen, Ralph, Benjamin Jurke, Thorsten Rahn, and Helmut Roschy. "Cohomology of line bundles: Applications." Journal of Mathematical Physics 53, no. 1 (January 2012): 012302. http://dx.doi.org/10.1063/1.3677646.

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BIGAS, MONTSERRAT TEIXIDOR I. "Stable extensions by line bundles." Journal für die reine und angewandte Mathematik (Crelles Journal) 1998, no. 502 (September 15, 1998): 163–72. http://dx.doi.org/10.1515/crll.1998.085.

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47

Kuwabara, Ruishi. "Isospectral connections on line bundles." Mathematische Zeitschrift 204, no. 1 (December 1990): 465–73. http://dx.doi.org/10.1007/bf02570886.

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Ambro, Florin, and Atsushi Ito. "Successive minima of line bundles." Advances in Mathematics 365 (May 2020): 107045. http://dx.doi.org/10.1016/j.aim.2020.107045.

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BISWAS, INDRANIL, and GEORG SCHUMACHER. "Line bundles and flat connections." Proceedings - Mathematical Sciences 127, no. 3 (May 4, 2017): 547–49. http://dx.doi.org/10.1007/s12044-017-0344-5.

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50

Ein, L., R. Lazarsfeld, M. Mustata, M. Nakamaye, and M. Popa. "Asymptotic Invariants of Line Bundles." Pure and Applied Mathematics Quarterly 1, no. 2 (2005): 379–403. http://dx.doi.org/10.4310/pamq.2005.v1.n2.a8.

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