Homogeneous affine surfaces: Moduli spaces

Affine Embeddings of Homogeneous Spaces

Let G be a reductive algebraic group and H a closed subgroup of G. An affine embedding of the homogeneous space G/H is an affine G-variety with an open G-orbit isomorphic to G/H . The homogeneous space G/H admits an affine embedding if and only if G/H is a quasi-affine algebraic variety. We start with some basic properties of affine embeddings and consider the cases, where the theory is well-de...

Zero - Entropy Affine Maps on Homogeneous Spaces

Computation of the Cartan Spaces of Affine Homogeneous Spaces

Let G be a reductive algebraic group and H its reductive subgroup. Fix a Borel subgroup B ⊂ G and a maximal torus T ⊂ B. The Cartan space aG,G/H is, by definition, the subspace of Lie(T )∗ generated by the weights of B-semiinvariant rational functions on G/H . We compute the spaces aG,G/H.

K3 surfaces: moduli spaces and Hilbert schemes

LetX be an algebraicK3 surface. Fix an ample divisorH onX ,L ∈ Pic(X) and c2 ∈ Z. Let MH(r;L, c2) be the moduli space of rank r, H-stable vector bundles E over X with det(E) = L and c2(E) = c2. The goal of this paper is to determine invariants (r; c1, c2) for which MH(r;L, c2) is birational to some Hilbert scheme Hilb(X).

Beauville Surfaces, Moduli Spaces and Finite Groups

In this paper we give the asymptotic growth of the number of connected components of the moduli space of surfaces of general type corresponding to certain families of Beauville surfaces with group either PSL(2, p), or an alternating group, or a symmetric group or an abelian group. We moreover extend these results to regular surfaces isogenous to a higher product of curves.