Let $A$ be an affine variety inside a complex $N$ dimensional
vector space which either has an isolated singularity at the origin
or is smooth at the origin. The intersection of $A$ with a very
small sphere turns out to be a contact manifold called...
In this talk, we will discuss the local geometry of the closure
of orbit space that parametrising smooth Fano manifolds inside
certain Chow/Hilbert scheme. In particular, we will discuss the
separatedness of the moduli of smoothable $K$-polystable $...
In 1984 Hirzebruch constructed the first examples of smooth
toroidal compactifications of ball quotients with non-nef canonical
divisor. In this talk, I will show that if the dimension is greater
or equal than three then such examples cannot exist...
Let \(Y\) be a smooth rational surface and let \(D\) be an
effective divisor linearly equivalent to \(-K_Y\), such that \(D\)
is a cycle of smooth rational curves. Such pairs \((Y,D)\) arise in
many contexts, for example in the study of...
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...
