Complete subvarieties in moduli spaces of rank 2 stable sheaves on smooth projective curves and surfaces
نویسنده
چکیده
The aim of this paper is to prove the existence of large complete subvarieties in moduli spaces of rank two stable sheaves with arbitrary c1 and sufficiently large c2, on algebraic surfaces. Then we study the restriction of these sheaves to curves of high degree embedded in the surface. In the final section we gives a relation with the spin strata defined by Pidstrigach and Tyurin.
منابع مشابه
Euler Characteristics of Moduli Spaces of Torsion Free Sheaves on Toric Surfaces
As an application of the combinatorial description of fixed point loci of moduli spaces of sheaves on toric varieties derived in [Koo], we study generating functions of Euler characteristics of moduli spaces of μ-stable torsion free sheaves on nonsingular complete toric surfaces. We express the generating function in terms of Euler characteristics of configuration spaces of linear subspaces. Th...
متن کاملMurphy’s Law in Algebraic Geometry: Badly-behaved Deformation Spaces
We consider the question: “How bad can the deformation space of an object be?” The answer seems to be: “Unless there is some a priori reason otherwise, the deformation space may be as bad as possible.” We show this for a number of important moduli spaces. More precisely, every singularity of finite type overZ (up to smooth parameters) appears on: the Hilbert scheme of curves in projective space...
متن کاملStable Rank-2 Bundles on Calabi-yau Manifolds
Recently there is a surge of research interest in the construction of stable vector bundles on Calabi-Yau manifolds motivated by questions from string theory. An interesting aspect of the moduli spaces of stable sheaves on Calabi-Yau manifolds is their relation to the higher dimensional gauge theory studied by Donaldson, R. Thomas and Tian et al. [D-T, Tho, Tia]. A holomorphic Casson invariant ...
متن کاملThe Nef Cone of the Moduli Space of Sheaves and Strong Bogomolov Inequalities
Let (X, H) be a polarized, smooth, complex projective surface, and let v be a Chern character on X with positive rank and sufficiently large discriminant. In this paper, we compute the Gieseker wall for v in a slice of the stability manifold of X. We construct explicit curves parameterizing non-isomorphic Gieseker stable sheaves of character v that become S-equivalent along the wall. As a corol...
متن کاملThe First Two Betti Numbers of the Moduli Spaces of Vector Bundles on Surfaces
This paper is a continuation of our effort in understanding the geometry of the moduli space of stable vector bundles. For any polarized smooth projective surface (X,H) and for any choice of (I, d) ∈ Pic(X) × H(X,Z), there is a coarse moduli space M(I, d) of rank two μ-stable (with respect to H) locally free sheaves E of ∧E ∼= I and c2(E) = d. This moduli space has been studied extensively rece...
متن کامل