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Journal articles

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 (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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2

Choi, Jinwon, and Kiryong Chung. "Cohomology bounds for sheaves of dimension one." International Journal of Mathematics 25, no. 11 (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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3

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

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4

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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5

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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6

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 (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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7

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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8

Schmitt, Alexander. "Stability Parameters for Quiver Sheaves." International Mathematics Research Notices 2020, no. 20 (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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9

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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10

Chen, Huachen. "O’Grady’s birational maps and strange duality via wall-hitting." International Journal of Mathematics 30, no. 09 (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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