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Academic literature on the topic 'Semistable sheaves'

Author: Grafiati

Published: 14 March 2023

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Journal articles on the topic "Semistable sheaves"

1

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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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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Choi, Jinwon, and Kiryong Chung. "Cohomology bounds for sheaves of dimension one." International Journal of Mathematics 25, no. 11 (October 2014): 1450103. http://dx.doi.org/10.1142/s0129167x14501031.

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We find sharp bounds on h0(F) for one-dimensional semistable sheaves F on a projective variety X. When X is the projective plane ℙ2, we study the stratification of the moduli space by the spectrum of sheaves. We show that the deepest stratum is isomorphic to a closed subset of a relative Hilbert scheme. This provides an example of a family of semistable sheaves having the biggest dimensional global section space.

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Langer, Adrian. "Semistable sheaves in positive characteristic." Annals of Mathematics 159, no. 1 (January 1, 2004): 251–76. http://dx.doi.org/10.4007/annals.2004.159.251.

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Langer, Adrian. "On boundedness of semistable sheaves." Documenta Mathematica 27 (2022): 1–16. http://dx.doi.org/10.4171/dm/865.

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Andreatta, Fabrizio, and Adrian Iovita. "Semistable Sheaves and Comparison Isomorphisms in the Semistable Case." Rendiconti del Seminario Matematico della Università di Padova 128 (2012): 131–285. http://dx.doi.org/10.4171/rsmup/128-7.

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Patel, Deepam, Tobias Schmidt, and Matthias Strauch. "LOCALLY ANALYTIC REPRESENTATIONS OF VIA SEMISTABLE MODELS OF." Journal of the Institute of Mathematics of Jussieu 18, no. 1 (January 12, 2017): 125–87. http://dx.doi.org/10.1017/s1474748016000396.

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In this paper we study certain sheaves of $p$-adically complete rings of differential operators on semistable models of the projective line over the ring of integers in a finite extension $L$ of $\mathbb{Q}_{p}$. The global sections of these sheaves can be identified with (central reductions of) analytic distribution algebras of wide open congruence subgroups. It is shown that the global sections functor furnishes an equivalence between the categories of coherent module sheaves and finitely presented modules over the distribution algebras. Using the work of M. Emerton, we then describe admissible representations of $\text{GL}_{2}(L)$ in terms of sheaves on the projective limit of these formal schemes. As an application, we show that representations coming from certain equivariant line bundles on Drinfeld’s first étale covering of the $p$-adic upper half plane are admissible.

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ABE, TAKESHI. "SEMISTABLE SHEAVES WITH SYMMETRIC ON A QUADRIC SURFACE." Nagoya Mathematical Journal 227 (October 5, 2016): 86–159. http://dx.doi.org/10.1017/nmj.2016.50.

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For moduli spaces of sheaves with symmetric $c_{1}$ on a quadric surface, we pursue analogy to some results known for moduli spaces of sheaves on a projective plane. We define an invariant height, introduced by Drezet in the projective plane case, for moduli spaces of sheaves with symmetric $c_{1}$ on a quadric surface and describe the structure of moduli spaces of height zero. Then we study rational maps of moduli spaces of positive height to moduli spaces of representation of quivers, effective cones of moduli spaces, and strange duality for height-zero moduli spaces.

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Schmitt, Alexander. "Stability Parameters for Quiver Sheaves." International Mathematics Research Notices 2020, no. 20 (October 2020): 6666–98. http://dx.doi.org/10.1093/imrn/rnz162.

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Abstract In this paper, we will begin the systematic study of the influence of the choice of a faithful representation on the notion of (semi)stability for decorated principal bundles. We will prove boundedness for slope semistable quiver sheaves.

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Argáez, A. S. "Examples of Stability of Tensor Products in Positive Characteristic." ISRN Algebra 2011 (September 19, 2011): 1–12. http://dx.doi.org/10.5402/2011/659672.

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Let X be projective smooth variety over an algebraically closed field k and let ℰ, ℱ be μ-semistable locally free sheaves on X. When the base field is ℂ, using transcendental methods, one can prove that the tensor product is always a μ-semistable sheaf. However, this theorem is no longer true over positive characteristic; for an analogous theorem one needs the hypothesis of strong μ-semistability; nevertheless, this hypothesis is not a necessary condition. The objective of this paper is to construct, without the strongly μ-semistability hypothesis, a family of locally free sheaves with μ-stable tensor product.

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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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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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Dissertations / Theses on the topic "Semistable sheaves"

1

Abe, Takeshi. "BOUNDEDNESS OF SEMISTABLE SHEAVES OF RANK FOUR." 京都大学 (Kyoto University), 2001. http://hdl.handle.net/2433/150404.

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Scarponi, Danny. "Formes effectives de la conjecture de Manin-Mumford et réalisations du polylogarithme abélien." Thesis, Toulouse 3, 2016. http://www.theses.fr/2016TOU30100/document.

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Dans cette thèse nous étudions deux problèmes dans le domaine de la géométrie arithmétique, concernant respectivement les points de torsion des variétés abéliennes et le polylogarithme motivique sur les schémas abéliens. La conjecture de Manin-Mumford (démontrée par Raynaud en 1983) affirme que si A est une variété abélienne et X est une sous-variété de A ne contenant aucune translatée d'une sous-variété abélienne de A, alors X ne contient qu'un nombre fini de points de torsion de A. En 1996, Buium présenta une forme effective de la conjecture dans le cas des courbes. Dans cette thèse, nous montrons que l'argument de Buium peut être utilisé aussi en dimension supérieure pour prouver une version quantitative de la conjecture pour une classe de sous-variétés avec fibré cotangent ample étudiée par Debarre. Nous généralisons aussi à toute dimension un résultat sur la dispersion des relèvements p-divisibles non ramifiés obtenu par Raynaud dans le cas des courbes. En 2014, Kings and Roessler ont montré que la réalisation en cohomologie de Deligne analytique de la part de degré zéro du polylogarithme motivique sur les schémas abéliens peut être reliée aux formes de torsion analytique de Bismut-Koehler du fibré de Poincaré. Dans cette thèse, nous utilisons la théorie de l'intersection arithmétique dans la version de Burgos pour raffiner ce résultat dans le cas où la base du schéma abélien est propre
In this thesis we approach two independent problems in the field of arithmetic geometry, one regarding the torsion points of abelian varieties and the other the motivic polylogarithm on abelian schemes. The Manin-Mumford conjecture (proved by Raynaud in 1983) states that if A is an abelian variety and X is a subvariety of A not containing any translate of an abelian subvariety of A, then X can only have a finite number of points that are of finite order in A. In 1996, Buium presented an effective form of the conjecture in the case of curves. In this thesis, we show that Buium's argument can be made applicable in higher dimensions to prove a quantitative version of the conjecture for a class of subvarieties with ample cotangent studied by Debarre. Our proof also generalizes to any dimension a result on the sparsity of p-divisible unramified liftings obtained by Raynaud in the case of curves. In 2014, Kings and Roessler showed that the realisation in analytic Deligne cohomology of the degree zero part of the motivic polylogarithm on abelian schemes can be described in terms of the Bismut-Koehler higher analytic torsion form of the Poincaré bundle. In this thesis, using the arithmetic intersection theory in the sense of Burgos, we give a refinement of Kings and Roessler's result in the case in which the base of the abelian scheme is proper

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Chang, Chi-Kang, and 張繼剛. "Desingularized moduli spaces of torsion-free semistable sheaves on a K3 surface." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/fufjab.

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碩士
國立臺灣大學
數學研究所
106
Abstract The aim of this article is to study Kieran G. O’Grady’s paper "Desingularized moduli spaces of sheaves on a K3" in 1998, where the author constructs the moduli space of rank two torsion-free semistable sheaves on a non-singular K3 surface with c1 = 0 and c2 = c a even number not less then 4. This moduli space is denoted by Mc, which is a G.I.T. quotient from the Quot-scheme and is singular. By using Kirwan’s method of successive blow ups of the strictly semistable loci with reductive stabilizer, one can obtain a desingularization Mcc of Mc. What’s surprising is that when c = 4, there is a Mori extremal divisorial contraction of Mc4 so that the outcome is a hyperk¨ahler manifold Mf4. Moreover, the natural map from Mf4 to M4 is a morphism and hence a simplectic desingularization of M4. The hyperk¨ahler manifold Mf4 is not birational/deformation equivalence to another two typical constructions of HK manifolds: the Hilbert schemes of points and Kummer varieties. Key words: moduli space of sheaves, semistable sheaves, geometric invariant theory, symplectic resolution, hyperk¨ahler variety.

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Zowislok, Markus [Verfasser]. "On moduli spaces of semistable sheaves on K3 surfaces / vorgelegt von Markus Zowislok." 2010. http://d-nb.info/1003549594/34.

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Books on the topic "Semistable sheaves"

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Belmans, Pieter, Wei Ho, and Aise Johan de Jong, eds. Stacks Project Expository Collection. Cambridge University Press, 2022. http://dx.doi.org/10.1017/9781009051897.

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The Stacks Project Expository Collection (SPEC) compiles expository articles in advanced algebraic geometry, intended to bring graduate students and researchers up to speed on recent developments in the geometry of algebraic spaces and algebraic stacks. The articles in the text make explicit in modern language many results, proofs, and examples that were previously only implicit, incomplete, or expressed in classical terms in the literature. Where applicable this is done by explicitly referring to the Stacks project for preliminary results. Topics include the construction and properties of important moduli problems in algebraic geometry (such as the Deligne–Mumford compactification of the moduli of curves, the Picard functor, or moduli of semistable vector bundles and sheaves), and arithmetic questions for fields and algebraic spaces.

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Book chapters on the topic "Semistable sheaves"

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Schmitt, Alexander H. W. "Generically Semistable Linear Quiver Sheaves." In Springer Proceedings in Mathematics & Statistics, 393–415. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-67053-9_38.

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Guo, Haoyang, Sanal Shivaprasad, Dylan Spence, and Yueqiao Wu. "Boundedness of semistable sheaves." In Stacks Project Expository Collection, 126–62. Cambridge University Press, 2022. http://dx.doi.org/10.1017/9781009051897.006.

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