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The geometry of moduli spaces of sheaves
Preface to the second edition Preface to the first edition Introduction Part I. General Theory: 1. Preliminaries 2. Families of sheaves 3. The Grauert-Mullich Theorem 4. Moduli spaces Part II.Expand
On the Cobordism Class of the Hilbert Scheme of a Surface
Let S be a smooth projective surface and S [n] the Hilbert scheme of zerodimensional subschemes of S of length n. We proof that the class of S [n] in the complex cobordism ring depends only on theExpand
Chern classes of tautological sheaves on Hilbert schemes of points on surfaces
Abstract. We give an algorithmic description of the action of the Chern classes of tautological bundles on the cohomology of Hilbert schemes of points on a smooth surface within the framework ofExpand
The cup product of Hilbert schemes for K3 surfaces
Abstract.To any graded Frobenius algebra A we associate a sequence of graded Frobenius algebras A[n] so that there is canonical isomorphism of rings (H*(X;ℚ)[2])[n]≅H*(X[n];ℚ)[2n] for the HilbertExpand
Singular symplectic moduli spaces
Moduli spaces of semistable sheaves on a K3 or abelian surface with respect to a general ample divisor are shown to be locally factorial, with the exception of symmetric products of a K3 or abelianExpand
Stable pairs on curves and surfaces
We describe stability conditions for pairs consisting of a coherent sheaf and a homomorphism to a fixed coherent sheaf on a projective variety. The corresponding moduli spaces are constructed forExpand
Irreducibility of the punctual quotient scheme of a surface
AbstractIt is shown that the punctual quotient schemeQlr parametrizing all zero-dimensional quotients $$\mathcal{O}_{A^2 }^{ \oplus ^r } \to T$$ of lengthl and supported at some fixed point O∈A2 inExpand
On the symplectic eightfold associated to a Pfaffian cubic fourfold
We show that the irreducible holomorphic symplectic eightfold Z associated to a cubic fourfold Y not containing a plane is deformation-equivalent to the Hilbert scheme of four points on a K3 surface.Expand
Slodowy slices and universal Poisson deformations
Abstract We classify the nilpotent orbits in a simple Lie algebra for which the restriction of the adjoint quotient map to a Slodowy slice is the universal Poisson deformation of its central fibre.Expand