scholarly journals Moduli spaces of 1-dimensional semi-stable sheaves and strange duality on P2

2017 ◽  
Vol 318 ◽  
pp. 130-157 ◽  
Author(s):  
Yao Yuan
Keyword(s):  
Moduli Spaces ◽  
Stable Sheaves ◽  
Strange Duality

scholarly journals Moduli spaces of stable sheaves over quasi-polarized surfaces, and the relative Strange Duality morphism

2021 ◽  
Vol Volume 5 ◽  
Author(s):  
Svetlana Makarova
Keyword(s):  
Moduli Spaces ◽  
K3 Surfaces ◽  
Stable Sheaves ◽  
Strange Duality ◽  
Projective Surfaces

The main result of the present paper is a construction of relative moduli spaces of stable sheaves over the stack of quasipolarized projective surfaces. For this, we use the theory of good moduli spaces, whose study was initiated by Alper. As a corollary, we extend the relative Strange Duality morphism to the locus of quasipolarized K3 surfaces.

scholarly journals On the Singular Sheaves in the Fine Simpson Moduli Spaces of 1-dimensional Sheaves

2017 ◽  
Vol 60 (3) ◽  
pp. 522-535 ◽  
Author(s):  
Oleksandr Iena ◽  
Alain Leytem
Keyword(s):  
Projective Plane ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Blow Up ◽  
Line Bundles ◽  
Hilbert Polynomial ◽  
Stable Sheaves ◽  
Closed Subvariety

AbstractIn the Simpson moduli space M of semi-stable sheaves with Hilbert polynomial dm − 1 on a projective plane we study the closed subvariety M' of sheaves that are not locally free on their support. We show that for d ≥4 , it is a singular subvariety of codimension 2 in M. The blow up of M along M' is interpreted as a (partial) modification of M \ M' by line bundles (on support).

STABLE RANK-2 BUNDLES ON CALABI–YAU MANIFOLDS

2003 ◽  
Vol 14 (10) ◽  
pp. 1097-1120 ◽  
Author(s):  
WEI-PING LI ◽  
ZHENBO QIN
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Double Cover ◽  
Stable Rank ◽  
Chern Classes ◽  
Canonical Divisor ◽  
Rank 2 ◽  
Stable Sheaves ◽  
Rank 2 Bundles ◽  
Calabi Yau Manifolds

In this paper, we apply the technique of chamber structures of stability polarizations to construct the full moduli space of rank-2 stable sheaves with certain Chern classes on Calabi–Yau manifolds which are anti-canonical divisor of ℙ1×ℙn or a double cover of ℙ1×ℙn. These moduli spaces are isomorphic to projective spaces. As an application, we compute the holomorphic Casson invariants defined by Donaldson and Thomas.

scholarly journals Stable Sheaves on a Smooth Quadric Surface with Linear Hilbert Bipolynomials

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Edoardo Ballico ◽  
Sukmoon Huh
Keyword(s):  
Moduli Spaces ◽  
Free Resolution ◽  
Quadric Surface ◽  
Special Cases ◽  
Stable Sheaves ◽  
Smooth Quadric Surface

We investigate the moduli spaces of stable sheaves on a smooth quadric surface with linear Hilbert bipolynomial in some special cases and describe their geometry in terms of the locally free resolution of the sheaves.

K3 Surfaces

2007 ◽  
Author(s):  
D. Huybrechts
Keyword(s):  
Moduli Spaces ◽  
Special Class ◽  
K3 Surfaces ◽  
Derived Categories ◽  
K3 Surface ◽  
Hodge Structures ◽  
Surface Theory ◽  
Torelli Theorem ◽  
Stable Sheaves ◽  
Moduli Theory

After abelian varieties, K3 surfaces are the second most interesting special class of varieties. These have a rich internal geometry and a highly interesting moduli theory. Paralleling the famous Torelli theorem, results from Mukai and Orlov show that two K3 surfaces have equivalent derived categories precisely when their cohomologies are isomorphic weighing two Hodge structures. Their techniques also give an almost complete description of the cohomological action of the group of autoequivalences of the derived category of a K3 surface. The basic definitions and fundamental facts from K3 surface theory are recalled. As moduli spaces of stable sheaves on K3 surfaces are crucial for the argument, a brief outline of their theory is presented.

T-dual solutions of the Hull–Strominger system on non-Kähler threefolds

2020 ◽  
Vol 2020 (766) ◽  
pp. 137-150
Author(s):  
Mario Garcia-Fernandez
Keyword(s):  
Moduli Spaces ◽  
Tangent Bundle ◽  
Analytical Methods ◽  
Existence Of Solutions ◽  
K3 Surfaces ◽  
Dual Solutions ◽  
K3 Surface ◽  
Yang Mills ◽  
Torus Bundles ◽  
Stable Sheaves

AbstractWe construct new examples of solutions of the Hull–Strominger system on non-Kähler torus bundles over K3 surfaces, with the property that the connection {\nabla} on the tangent bundle is Hermite–Yang–Mills. With this ansatz for the connection {\nabla}, we show that the existence of solutions reduces to known results about moduli spaces of slope-stable sheaves on a K3 surface, combined with elementary analytical methods. We apply our construction to find the first examples of T-dual solutions of the Hull–Strominger system on compact non-Kähler manifolds with different topology.

O’Grady’s birational maps and strange duality via wall-hitting

2019 ◽  
Vol 30 (09) ◽  
pp. 1950044
Author(s):  
Huachen Chen
Keyword(s):  
Moduli Spaces ◽  
Hodge Structure ◽  
Duke Math ◽  
K3 Surface ◽  
Birational Maps ◽  
Moduli Spaces Of Sheaves ◽  
Wall Crossing ◽  
Moduli Of Sheaves ◽  
Ideal Sheaves ◽  
Strange Duality

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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