scholarly journals The Betti numbers of the moduli space of stable sheaves of rank2 on P2.

1994 ◽  
Vol 1994 (453) ◽  
pp. 193-220 ◽  
Keyword(s):  
Moduli Space ◽  
Betti Numbers ◽  
Stable Sheaves

scholarly journals Moduli of stable sheaves supported on curves of genus three contained in a quadric surface

2020 ◽  
Vol 20 (4) ◽  
pp. 507-522
Author(s):  
Mario Maican
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Betti Numbers ◽  
Free Resolutions ◽  
Quadric Surface ◽  
Arithmetic Genus ◽  
Blow Down ◽  
Stable Sheaves ◽  
Stable Pairs ◽  
Smooth Quadric Surface

AbstractWe study the moduli space of stable sheaves of Euler characteristic 1 supported on curves of arithmetic genus 3 contained in a smooth quadric surface. We show that this moduli space is rational. We compute its Betti numbers by studying the variation of the moduli spaces of α-semi-stable pairs. We classify the stable sheaves using locally free resolutions or extensions. We give a global description: the moduli space is obtained from a certain flag Hilbert scheme by performing two flips followed by a blow-down.

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).

scholarly journals Perverse Coherent Sheaves on Blow-ups at Codimension 2 Loci

2019 ◽  
Author(s):  
Naoki Koseki
Keyword(s):  
Moduli Space ◽  
Hilbert Scheme ◽  
Projective Variety ◽  
Blow Up ◽  
Smooth Projective Variety ◽  
Coherent Sheaves ◽  
Codimension Two ◽  
Higher Dimensional ◽  
Stable Sheaves ◽  
Closed Subvariety

Abstract Let $f \colon X \to Y$ be the blow-up of a smooth projective variety $Y$ along its codimension two smooth closed subvariety. In this paper, we show that the moduli space of stable sheaves on $X$ and $Y$ are connected by a sequence of flip-like diagrams. The result is a higher dimensional generalization of the result of Nakajima and Yoshioka, which is the case of $\dim Y=2$. As an application of our general result, we study the birational geometry of the Hilbert scheme of two points.

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 The derived moduli space of stable sheaves

2014 ◽  
Vol 8 (4) ◽  
pp. 781-812 ◽  
Author(s):  
Kai Behrend ◽  
Ionut Ciocan-Fontanine ◽  
Junho Hwang ◽  
Michael Rose
Keyword(s):  
Moduli Space ◽  
Stable Sheaves

scholarly journals Singularities on the 2-Dimensional Moduli Spaces of Stable Sheaves on K3 Surfaces

2003 ◽  
Vol 14 (08) ◽  
pp. 837-864 ◽  
Author(s):  
Nobuaki Onishi ◽  
Kōta Yoshioka
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
K3 Surfaces ◽  
Double Points ◽  
Exceptional Locus ◽  
Stable Sheaves

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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