Topology of Algebraic Varieties (TAV)

We discuss the universal triviality of the \(\mathrm{CH}_0\)-group of cubic hypersurfaces, or equivalently the existence of a Chow-theoretic decomposition of their diagonal. The motivation is the study of stable irrationality for these varieties...

Tate's conjecture for divisors on algebraic varieties can be rephrased as a finiteness statement for certain families of polarized varieties with unbounded degrees. In the case of abelian varieties, the geometric part of these finiteness statements...

I will try to explain some intuitions and some history about (mixed) Hodge theory. Warning: the experts will not learn anything new.

For an odd integer \(n > 3\) the data of generic n-dimensional subspace of the space of skew bilinear forms on an n-dimensional vector space define two different Calabi-Yau varieties of dimension \(n-4\). Specifically, one is a complete intersection...

Being the natural generalization of K3 surfaces, hyperkaehler varieties, also known as irreducible holomorphic symplectic varieties, are one of the building blocks of smooth projective varieties with trivial canonical bundle. One of the guiding...

A cusp singularity is an isolated surface singularity whose minimal resolution is a cycle of smooth rational curves meeting transversely. Cusp singularities come in naturally dual pairs. In the 1980's Looijenga conjectured that a cusp singularity is...

The aim of this talk is to study a class of singularities of moduli spaces of sheaves on K3 surfaces by means of Nakajima quiver varieties. The singularities in question arise from the choice of a non generic polarization, with respect to which we...

The Lipman-Zariski conjecture states that if the tangent sheaf of a complex variety is locally free then the variety is smooth. In joint work with Patrick Graf we prove that this holds whenever an extension theorem for differential 1-forms holds, in...

In many examples of moduli stacks which come equipped with a notion of stable points, one tests stability by considering "iso-trivial one parameter degenerations" of a point in the stack. To such a degeneration one can often associate a real number...

It is classical to study the geometry of projective varieties over algebraically closed fields through the properties of various positive cones of divisors or curves. Several counterexamples have shifted attention from the higher (co)dimensional...