Consider a smooth complex projective variety \(M\). To
understand the group of birational transformations (resp. regular
automorphisms) of \(M\), one can use tools from Hodge theory,
dynamical systems, and geometric group theory. I shall try
to...
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...
Consider a smooth complex projective variety \(M\). To
understand the group of birational transformations (resp. regular
automorphisms) of \(M\), one can use tools from Hodge theory,
dynamical systems, and geometric group theory. I shall try
to...
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...
