4 papers · 1 filter
Semicontinuity of Gauss maps and the Schottky problem
Giulio Codogni, Thomas Krämer
We show that the degree of Gauss maps on abelian varieties is semicontinuous in families, and we study its jump loci. As an application we obtain that in the case of theta divisors…
Theta divisors whose Gauss map has a fiber of positive dimension
Robert Auffarth, Giulio Codogni
We construct families of principally polarized abelian varieties whose theta divisor is irreducible and contains an abelian subvariety. These families are used to construct example…
Positivity of the CM line bundle for families of K-stable klt Fano varieties
Giulio Codogni, Zsolt Patakfalvi
The Chow-Mumford (CM) line bundle is a functorial line bundle on the base of any family of klt Fano varieties. It is conjectured that it yields a polarization on the moduli space o…
Tits buildings and K-stability
Giulio Codogni
A polarized variety is K-stable if, for any test configuration, the Donaldson-Futaki invariant is positive. In this paper, inspired by classical geometric invariant theory, we desc…