Special Year 2014-15: The Topology of Algebraic Varieties

KSBA (Kollár-Shepherd-Barron-Alexeev) stable pairs are higher dimensional generalizations of (weighted) stable pointed curves. I will present a joint work in progress with Sándor Kovács on proving the projectivity of this moduli space, by showing...

I will first discuss a relation between the cohomology groups (with rational coefficients) of the compactified Jacobian and those of the Hilbert schemes of a projective irreducible curve $C$ with planar singularities, which extends the classical...

We study the restriction map to the closed fiber for the Chow group of zero-cycles over a complete discrete valuation ring. It turns out that, for proper families of varieties and for certain finite coefficients, the restriction map is an...

Tropical geometry gives a new approach to understanding old questions about algebraic curves and their moduli spaces, synthesizing techniques that range from Berkovich spaces to elementary combinatorics. I will discuss an outline of this method...

The Torelli map associates to a genus g curve its Jacobian - a $g$-dimensional principally polarized abelian variety. It turns out, by the works of Mumford and Namikawa in the 1970s (resp. Alexeev and Brunyate in 2010s), that the Torelli map extends...

We will first quickly recall basic facts on the tree of SL_2 over a field K with a discrete valuation v, following Serre's book. We will then generalize the geometric interpretation given in that book for curves to a higher dimensional situation...

For low degree K3 surfaces there are several way of constructing and compactifying the moduli space (via period maps, via GIT, or via KSBA). In the case of degree 2 K3 surface, the relationship between various compactifications is well understood by...

We will first quickly recall basic facts on the tree of SL_2 over a field K with a discrete valuation v, following Serre's book. We will then generalize the geometric interpretation given in that book for curves to a higher dimensional situation...

Inspired by the elementary notion of graph chordality, we introduce the notion of toric chordality, which naturally gives a tool to to study the geometry and combinatorics of cohomology classes of toric varieties and the weight algebras of polytopes...