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Автор: Grafiati

Опубліковано: 14 березня 2023

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1

Qin, Zhenbo. "Simple sheaves versus stable sheaves on algebraic surfaces." Mathematische Zeitschrift 209, no. 1 (January 1992): 559–79. http://dx.doi.org/10.1007/bf02570854.

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2

Hille, Lutz, and Markus Perling. "Exceptional sequences of invertible sheaves on rational surfaces." Compositio Mathematica 147, no. 4 (March 18, 2011): 1230–80. http://dx.doi.org/10.1112/s0010437x10005208.

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Анотація:

AbstractIn this article we consider exceptional sequences of invertible sheaves on smooth complete rational surfaces. We show that to every such sequence one can associate a smooth complete toric surface in a canonical way. We use this structural result to prove various theorems on exceptional and strongly exceptional sequences of invertible sheaves on rational surfaces. We construct full strongly exceptional sequences for a large class of rational surfaces. For the case of toric surfaces we give a complete classification of full strongly exceptional sequences of invertible sheaves.

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3

HALIC, MIHAI, and ROSHAN TAJAROD. "A cohomological splitting criterion for locally free sheaves on arithmetically Cohen–Macaulay surfaces." Mathematical Proceedings of the Cambridge Philosophical Society 155, no. 3 (July 3, 2013): 517–27. http://dx.doi.org/10.1017/s0305004113000406.

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AbstractIn this paper we obtain a cohomological splitting criterion for locally free sheaves on arithmetically Cohen–Macaulay surfaces with cyclic Picard group, which is similar to Horrocks' splitting criterion for locally free sheaves on projective spaces. We also recover a duality property which identifies a general K3 surface with a certain moduli space of stable sheaves on it, and obtain examples of stable, arithmetically Cohen–Macaulay, locally free sheaves of rank two on general surfaces of degree at least five in ${\mathbb P}^3$.

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4

Scalise, Jacopo Vittorio. "Framed symplectic sheaves on surfaces." International Journal of Mathematics 29, no. 01 (January 2018): 1850007. http://dx.doi.org/10.1142/s0129167x18500076.

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A framed symplectic sheaf on a smooth projective surface [Formula: see text] is a torsion-free sheaf [Formula: see text] together with a trivialization on a divisor [Formula: see text] and a morphism [Formula: see text] satisfying some additional conditions. We construct a moduli space for framed symplectic sheaves on a surface, and present a detailed study for [Formula: see text]. In this case, the moduli space is irreducible and admits an ADHM-type description and a birational proper map onto the space of framed symplectic ideal instantons.

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5

Göttsche, Lothar, and Martijn Kool. "Sheaves on surfaces and virtual invariants." Surveys in Differential Geometry 24, no. 1 (2019): 67–116. http://dx.doi.org/10.4310/sdg.2019.v24.n1.a3.

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6

Rutherford, Dan, and Michael Sullivan. "Sheaves via augmentations of Legendrian surfaces." Journal of Homotopy and Related Structures 16, no. 4 (October 9, 2021): 703–52. http://dx.doi.org/10.1007/s40062-021-00292-6.

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7

Kuleshov, S. A., and D. O. Orlov. "EXCEPTIONAL SHEAVES ON DEL PEZZO SURFACES." Russian Academy of Sciences. Izvestiya Mathematics 44, no. 3 (June 30, 1995): 479–513. http://dx.doi.org/10.1070/im1995v044n03abeh001609.

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8

Shvartsman, O. V. "FreeG-sheaves on closed Riemann surfaces." Russian Mathematical Surveys 54, no. 6 (December 31, 1999): 1263–64. http://dx.doi.org/10.1070/rm1999v054n06abeh000246.

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9

Bertram, Aaron, and Cristian Martinez. "Change of Polarization for Moduli of Sheaves on Surfaces as Bridgeland Wall-crossing." International Mathematics Research Notices 2020, no. 7 (April 25, 2018): 2007–33. http://dx.doi.org/10.1093/imrn/rny065.

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Анотація:

Abstract We prove that the “Thaddeus flips” of L-twisted sheaves constructed by Matsuki and Wentworth explaining the change of polarization for Gieseker semistable sheaves on a surface can be obtained via Bridgeland wall-crossing. Similarly, we realize the change of polarization for moduli spaces of one-dimensional Gieseker semistable sheaves on a surface by varying a family of stability conditions.

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10

Yoshioka, Kōta. "Some notes on the moduli of stable sheaves on elliptic surfaces." Nagoya Mathematical Journal 154 (1999): 73–102. http://dx.doi.org/10.1017/s0027763000025319.

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Анотація:

AbstractIn this paper, we shall consider the birational structure of moduli of stable sheaves on elliptic surfaces, which is a generalization of Friedman’s results to higher rank cases. As applications, we show that some moduli spaces of stable sheaves on ℙ2 are rational. We also compute the Picard groups of those on Abelian surfaces.

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11

Chen, Huachen. "O’Grady’s birational maps and strange duality via wall-hitting." International Journal of Mathematics 30, no. 09 (August 2019): 1950044. http://dx.doi.org/10.1142/s0129167x19500447.

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Анотація:

We prove that O’Grady’s birational maps [K. G O’Grady, The weight-two Hodge structure of moduli spaces of sheaves on a K3 surface, J. Algebr. Geom. 6(4) (1997) 599–644] between moduli of sheaves on an elliptic K3 surface can be interpreted as intermediate wall-crossing (wall-hitting) transformations at so-called totally semistable walls, studied by Bayer and Macrì [A. Bayer and E. Macrì, MMP for moduli of sheaves on K3s via wall-crossing: nef and movable cones, Lagrangian fibrations, Inventiones Mathematicae 198(3) (2014) 505–590]. As a key ingredient, we describe the first totally semistable wall for ideal sheaves of [Formula: see text] points on the elliptic [Formula: see text]. As an application, we give new examples of strange duality isomorphisms, based on a result of Marian and Oprea [A. Marian and D. Oprea, Generic strange duality for K3 surfaces, with an appendix by Kota Yoshioka, Duke Math. J. 162(8) (2013) 1463–1501].

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12

Coskun, Izzet, and Jack Huizenga. "Existence of semistable sheaves on Hirzebruch surfaces." Advances in Mathematics 381 (April 2021): 107636. http://dx.doi.org/10.1016/j.aim.2021.107636.

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13

Ballico, Edoardo. "Vector bundles, reflexive sheaves and algebraic surfaces." Rendiconti del Seminario Matematico e Fisico di Milano 60, no. 1 (December 1990): 71–91. http://dx.doi.org/10.1007/bf02925079.

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14

Sawon, Justin. "Moduli spaces of sheaves on K3 surfaces." Journal of Geometry and Physics 109 (November 2016): 68–82. http://dx.doi.org/10.1016/j.geomphys.2016.02.017.

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15

Sun, Xiaotao. "On relative canonical sheaves of arithmetic surfaces." Mathematische Zeitschrift 223, no. 1 (September 1996): 709–23. http://dx.doi.org/10.1007/bf02621626.

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16

Sun, Xiaotao. "On relative canonical sheaves of arithmetic surfaces." Mathematische Zeitschrift 223, no. 4 (December 1996): 709–23. http://dx.doi.org/10.1007/pl00004282.

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17

Marian, Alina, and Dragos Oprea. "Sheaves on abelian surfaces and strange duality." Mathematische Annalen 343, no. 1 (August 7, 2008): 1–33. http://dx.doi.org/10.1007/s00208-008-0262-z.

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18

Bruzzo, Ugo, and Dimitri Markushevish. "Moduli of framed sheaves on projective surfaces." Documenta Mathematica 16 (2011): 399–410. http://dx.doi.org/10.4171/dm/336.

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19

Onishi, Nobuaki, and Kōta Yoshioka. "Singularities on the 2-Dimensional Moduli Spaces of Stable Sheaves on K3 Surfaces." International Journal of Mathematics 14, no. 08 (October 2003): 837–64. http://dx.doi.org/10.1142/s0129167x03002022.

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Анотація:

We consider the singuralities of 2-dimensional moduli spaces of semi-stable sheaves on k3 surfaces. We show that the moduli space is normal, in particular the siguralities are rational double points. We also describe the exceptional locus on the resolution in terms of exceptional sheaves.

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20

Camere, Chiara, Grzegorz Kapustka, Michał Kapustka, and Giovanni Mongardi. "Verra Four-Folds, Twisted Sheaves, and the Last Involution." International Mathematics Research Notices 2019, no. 21 (February 1, 2018): 6661–710. http://dx.doi.org/10.1093/imrn/rnx327.

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Анотація:

Abstract We study the geometry of some moduli spaces of twisted sheaves on K3 surfaces. In particular we introduce induced automorphisms from a K3 surface on moduli spaces of twisted sheaves on this K3 surface. As an application we prove the unirationality of moduli spaces of irreducible holomorphic symplectic manifolds of K3[2]-type admitting non-symplectic involutions with invariant lattices U(2) ⊕ D4(−1) or U(2) ⊕ E8(−2). This complements the results obtained in [43], [13], and the results from [29] about the geometry of irreducible holomorphic symplectic (IHS) four-folds constructed using the Hilbert scheme of (1, 1) conics on Verra four-folds. As a byproduct we find that IHS four-folds of K3[2]-type with Picard lattice U(2) ⊕ E8(−2) naturally contain non-nodal Enriques surfaces.

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21

Goller, Thomas, and Yinbang Lin. "Rank-one sheaves and stable pairs on surfaces." Advances in Mathematics 401 (June 2022): 108322. http://dx.doi.org/10.1016/j.aim.2022.108322.

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22

Yoshioka, Kōta. "A note on stable sheaves on Enriques surfaces." Tohoku Mathematical Journal 69, no. 3 (September 2017): 369–82. http://dx.doi.org/10.2748/tmj/1505181622.

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23

Verbitsky, Misha. "Coherent Sheaves on General K3 Surfaces and Tori." Pure and Applied Mathematics Quarterly 4, no. 3 (2008): 651–714. http://dx.doi.org/10.4310/pamq.2008.v4.n3.a3.

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24

Yoshioka, Kōta. "Moduli spaces of stable sheaves on Enriques surfaces." Kyoto Journal of Mathematics 58, no. 4 (December 2018): 865–914. http://dx.doi.org/10.1215/21562261-2017-0037.

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25

Qin, Zhenbo. "Moduli of simple rank-2 sheaves onK3-surfaces." manuscripta mathematica 79, no. 1 (December 1993): 253–65. http://dx.doi.org/10.1007/bf02568344.

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26

Yoshioka, Kōta. "Moduli spaces of stable sheaves on abelian surfaces." Mathematische Annalen 321, no. 4 (December 1, 2001): 817–84. http://dx.doi.org/10.1007/s002080100255.

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27

Langer, Adrian. "Chern classes of reflexive sheaves on normal surfaces." Mathematische Zeitschrift 235, no. 3 (November 1, 2000): 591–614. http://dx.doi.org/10.1007/s002090000149.

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28

Charles, François, and Eyal Markman. "The standard conjectures for holomorphic symplectic varieties deformation equivalent to Hilbert schemes of K3 surfaces." Compositio Mathematica 149, no. 3 (February 7, 2013): 481–94. http://dx.doi.org/10.1112/s0010437x12000607.

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Анотація:

AbstractWe prove the standard conjectures for complex projective varieties that are deformations of the Hilbert scheme of points on a K3 surface. The proof involves Verbitsky’s theory of hyperholomorphic sheaves and a study of the cohomology algebra of Hilbert schemes of K3 surfaces.

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29

Toda, Yukinobu. "Stability conditions and birational geometry of projective surfaces." Compositio Mathematica 150, no. 10 (July 17, 2014): 1755–88. http://dx.doi.org/10.1112/s0010437x14007337.

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Анотація:

AbstractWe show that the minimal model program on any smooth projective surface is realized as a variation of the moduli spaces of Bridgeland stable objects in the derived category of coherent sheaves.

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30

HEIN, GEORG, and DAVID PLOOG. "POSTNIKOV-STABILITY FOR COMPLEXES ON CURVES AND SURFACES." International Journal of Mathematics 23, no. 02 (February 2012): 1250048. http://dx.doi.org/10.1142/s0129167x12500486.

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Анотація:

We present a novel notion of stable objects in the derived category of coherent sheaves on a smooth projective variety. As one application we compactify a moduli space of stable bundles using genuine complexes.

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31

Bandiera, Ruggero, Marco Manetti, and Francesco Meazzini. "Deformations of Polystable Sheaves on Surfaces: Quadraticity Implies Formality." Moscow Mathematical Journal 22, no. 2 (2022): 239–63. http://dx.doi.org/10.17323/1609-4514-2022-22-2-239-263.

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32

Hauzer, Marcin. "On moduli spaces of semistable sheaves on Enriques surfaces." Annales Polonici Mathematici 99, no. 3 (2010): 305–21. http://dx.doi.org/10.4064/ap99-3-7.

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33

Manschot, Jan, and Sergey Mozgovoy. "Intersection cohomology of moduli spaces of sheaves on surfaces." Selecta Mathematica 24, no. 5 (August 14, 2018): 3889–926. http://dx.doi.org/10.1007/s00029-018-0431-1.

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34

Corrêa, M. "Rank two nilpotent co-Higgs sheaves on complex surfaces." Geometriae Dedicata 183, no. 1 (January 19, 2016): 25–31. http://dx.doi.org/10.1007/s10711-016-0141-9.

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35

Ingalls, C., and M. Khalid. "RANK 2 SHEAVES ON K3 SURFACES: A SPECIAL CONSTRUCTION." Quarterly Journal of Mathematics 64, no. 2 (June 1, 2012): 443–70. http://dx.doi.org/10.1093/qmath/has009.

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36

Manschot, Jan. "BPS Invariants of Semi-Stable Sheaves on Rational Surfaces." Letters in Mathematical Physics 103, no. 8 (April 21, 2013): 895–918. http://dx.doi.org/10.1007/s11005-013-0624-7.

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37

Bruzzo, Ugo, Dimitri Markushevich, and Alexander Tikhomirov. "Uhlenbeck–Donaldson compactification for framed sheaves on projective surfaces." Mathematische Zeitschrift 275, no. 3-4 (June 13, 2013): 1073–93. http://dx.doi.org/10.1007/s00209-013-1170-9.

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38

Yoshioka, Kōta. "A note on stable sheaves on Enriques surfaces II." manuscripta mathematica 153, no. 1-2 (August 26, 2016): 147–58. http://dx.doi.org/10.1007/s00229-016-0882-7.

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39

Collas, Benjamin, Michael Dettweiler, Stefan Reiter, and Will Sawin. "Monodromy of elliptic curve convolution, seven-point sheaves of G ₂ type, and motives of Beauville type." Journal für die reine und angewandte Mathematik (Crelles Journal) 2022, no. 784 (January 23, 2022): 1–26. http://dx.doi.org/10.1515/crelle-2021-0070.

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Анотація:

Abstract We study Tannakian properties of the convolution product of perverse sheaves on elliptic curves. We establish that for certain sheaves with unipotent local monodromy over seven points the corresponding Tannaka group is isomorphic to G 2 {G_{2}} . This monodromy approach generalizes a result of Katz on the existence of G 2 {G_{2}} -motives in the middle cohomology of deformations of Beauville surfaces.

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40

He, Guifang, Chunfu Sheng, Hongwei He, Rong Zhou, Ding Yuan, Xin Ning, and Fanggang Ning. "Mathematical and geometrical modeling of braided ropes bent over a sheave." Journal of Engineered Fibers and Fabrics 15 (January 2020): 155892502093972. http://dx.doi.org/10.1177/1558925020939726.

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As soft elements for force transmission, braided fiber ropes play important roles in many fields where the fiber ropes are used bent over sheaves, while the relevant experiments are time-consuming and expensive. Computational simulation is a promising choice for evaluating the performance of fiber ropes when bent over a sheave. This article presents two methods that could be employed to build a model of braided rope bent over a sheave. One is the mathematical method which deduces the exact mathematical equations of braiding curves based on the Frenet–Serret frame. The spatial equations, considering the phase difference of strands in the same direction and the difference of strands’ projection in different directions, are discussed carefully. The final equation of braided strands is confirmed by modeling the braided rope in Maple® 17. The other method, which is inspired by the analysis of braiding movements, is based on the intersection of surfaces of braiding surface and helical surface which are introduced and defined based on the motion analysis of bobbins and take-up roller. The SolidWorks® 2018 is successfully employed to realize the modeling process.

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41

Yuan, Yao. "Strange Duality on Rational Surfaces II: Higher-Rank Cases." International Mathematics Research Notices 2020, no. 10 (June 22, 2018): 3153–200. http://dx.doi.org/10.1093/imrn/rny133.

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Abstract We study Le Potier’s strange duality conjecture on a rational surface. We focus on the strange duality map $SD_{c_n^r,L}$ that involves the moduli space of rank $r$ sheaves with trivial 1st Chern class and 2nd Chern class $n$, and the moduli space of one-dimensional sheaves with determinant $L$ and Euler characteristic 0. We show there is an exact sequence relating the map $SD_{c_r^r,L}$ to $SD_{c^{r-1}_{r},L}$ and $SD_{c_r^r,L\otimes K_X}$ for all $r\geq 1$ under some conditions on $X$ and $L$ that applies to a large number of cases on $\mathbb{P}^2$ or Hirzebruch surfaces. Also on $\mathbb{P}^2$ we show that for any $r>0$, $SD_{c^r_r,dH}$ is an isomorphism for $d=1,2$, injective for $d=3,$ and moreover $SD_{c_3^3,rH}$ and $SD_{c_3^2,rH}$ are injective. At the end we prove that the map $SD_{c_n^2,L}$ ($n\geq 2$) is an isomorphism for $X=\mathbb{P}^2$ or Fano rational-ruled surfaces and $g_L=3$, and hence so is $SD_{c_3^3,L}$ as a corollary of our main result.

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42

Bocklandt, Raf. "Toric systems and mirror symmetry." Compositio Mathematica 149, no. 11 (August 28, 2013): 1839–55. http://dx.doi.org/10.1112/s0010437x1300701x.

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AbstractIn their paper [Exceptional sequences of invertible sheaves on rational surfaces, Compositio Math. 147 (2011), 1230–1280], Hille and Perling associate to every cyclic full strongly exceptional sequence of line bundles on a toric weak del Pezzo surface a toric system, which defines a new toric surface. We interpret this construction as an instance of mirror symmetry and extend it to a duality on the set of toric weak del Pezzo surfaces equipped with a cyclic full strongly exceptional sequence.

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43

Budur, Nero, and Ziyu Zhang. "Formality conjecture for K3 surfaces." Compositio Mathematica 155, no. 5 (April 23, 2019): 902–11. http://dx.doi.org/10.1112/s0010437x19007206.

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Анотація:

We give a proof of the formality conjecture of Kaledin and Lehn: on a complex projective K3 surface, the differential graded (DG) algebra$\operatorname{RHom}^{\bullet }(F,F)$is formal for any sheaf$F$polystable with respect to an ample line bundle. Our main tool is the uniqueness of the DG enhancement of the bounded derived category of coherent sheaves. We also extend the formality result to derived objects that are polystable with respect to a generic Bridgeland stability condition.

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44

Inaba, Michi-Aki. "On the moduli of stable sheaves on a reducible projective scheme and examples on a reducible quadric surface." Nagoya Mathematical Journal 166 (June 2002): 135–81. http://dx.doi.org/10.1017/s0027763000008291.

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Анотація:

AbstractWe study the moduli space of stable sheaves on a reducible projective scheme by use of a suitable stratification of the moduli space. Each stratum is the moduli space of “triples”, which is the main object investigated in this paper. As an application, we can see that the relative moduli space of rank two stable sheaves on quadric surfaces gives a nontrivial example of the relative moduli space which is not flat over the base space.

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45

Lieblich, Max. "Twisted sheaves and the period-index problem." Compositio Mathematica 144, no. 1 (January 2008): 1–31. http://dx.doi.org/10.1112/s0010437x07003144.

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AbstractWe use twisted sheaves and their moduli spaces to study the Brauer group of a scheme. In particular, we (1) show how twisted methods can be efficiently used to re-prove the basic facts about the Brauer group and cohomological Brauer group (including Gabber’s theorem that they coincide for a separated union of two affine schemes), (2) give a new proof of de Jong’s period-index theorem for surfaces over algebraically closed fields, and (3) prove an analogous result for surfaces over finite fields. We also include a reduction of all period-index problems for Brauer groups of function fields over algebraically closed fields to characteristic zero, which (among other things) extends de Jong’s result to include classes of period divisible by the characteristic of the base field. Finally, we use the theory developed here to give counterexamples to a standard type of local-to-global conjecture for geometrically rational varieties over the function field of the projective plane.

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46

Sala, Francesco. "Symplectic structures on moduli spaces of framed sheaves on surfaces." Central European Journal of Mathematics 10, no. 4 (May 2, 2012): 1455–71. http://dx.doi.org/10.2478/s11533-012-0063-1.

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47

Langer, Adrian. "Moduli spaces and Castelnuovo-Mumford regularity of sheaves on surfaces." American Journal of Mathematics 128, no. 2 (2006): 373–417. http://dx.doi.org/10.1353/ajm.2006.0014.

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48

Buchdahl, Nicholas, Andrei Teleman, and Matei Toma. "A continuity theorem for families of sheaves on complex surfaces." Journal of Topology 10, no. 4 (October 19, 2017): 995–1028. http://dx.doi.org/10.1112/topo.12029.

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49

Yoshioka, Kōta. "Perverse coherent sheaves and Fourier–Mukai transforms on surfaces, I." Kyoto Journal of Mathematics 53, no. 2 (2013): 261–344. http://dx.doi.org/10.1215/21562261-2081234.

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50

Yoshioka, Kōta. "Perverse coherent sheaves and Fourier–Mukai transforms on surfaces, II." Kyoto Journal of Mathematics 55, no. 2 (June 2015): 365–459. http://dx.doi.org/10.1215/21562261-2871785.

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