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On the Invariant Hilbert schemes and Luna’s étale slice theorem
In this paper, we study local structures of invariant Hilbert schemes with Luna’s étale slice theorem. We prove that in some cases the invariant...
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Generating series of intersection numbers on Hilbert schemes of points
We compute some generating series of integrals related to tautological bundles on Hilbert schemes of points on surfaces S ...
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Tautological integrals on symmetric products of curves
We propose a conjecture on the generating series of Chern numbers of tautological bundles on symmetric products of curves and establish the rank 1...
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The Birational Geometry of Moduli Spaces
The purpose of these lecture notes is to introduce the basics of the birational geometry of moduli spaces to students who have taken an introductory...
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On Chow stability for algebraic curves
In the last decades there have been introduced different concepts of stability for projective varieties. In this paper we give a natural and...
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Equivariant Degenerations of Spherical Modules: Part II
We determine, under a certain assumption, the Alexeev–Brion moduli scheme M of affine spherical G -varieties with a prescribed weight monoid . In...
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Quotients of an affine variety by an action of a torus
Let X be an affine T -variety. We study two different quotients for the action of T on X : the toric Chow quotient X / C T and the toric Hilbert scheme H ....
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On the irreducibility of Hilbert scheme of surfaces of minimal degree
The article contains a new proof that the Hilbert scheme of irreducible surfaces of degree m in ℙ m +1 is irreducible except m = 4. In the case m = 4...
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Elliptic curves on spinor varieties
We prove irreducibility of the scheme of morphisms, of degree large enough, from a smooth elliptic curve to spinor varieties. We give an explicit...
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Nonabelian Jacobian of smooth projective surfaces-a survey
The nonabelian Jacobian J ( X ; L, d ) of a smooth projective surface X is inspired by the classical theory of Jacobian of curves. It is built as a...
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Monomial multiple structures
In this paper we study Cohen–Macaulay monomial multiple structures (non-reduced schemes) on a linear subspace of codimension two in projective space....
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Topological properties of Hilbert schemes of almost-complex fourfolds (I)
In this article, we study topological properties of Voisin’s Hilbert schemes of an almost-complex four-manifold X . We compute in this setting their...