POK0

Positivity of K-trivial varieties

01/04/2024 to 31/03/2027

Varieties with trivial canonical bundle – or K-trivial varieties – possess an
extremely rich geometry and lie at the center of all classification theories of projective varieties.
In recent years there have been major breakthroughs both in the theory itself and in related areas.
The goal of the project “Positivity of K-trivial varieties” (POK0) is to exploit these recent advances in a
collaborative effort in order to attack several fundamental questions concerning K-trivial varieties.

We focus more specifically on various positivity problems such as: (a) the Morrison--Kawamata cone conjecture and applications to minimal models; (b) the study of linear systems on K-trivial varieties and their properties: base loci and global generation, local positivity, abundance-conjecture-type problems, Fujita-conjecture type problems; (c) projective geometry of hyperkähler manifolds: higher syzygies and projective models of such varieties.

To achieve our goal, we bring together a group of researchers with different and complementary expertise, relying both on well-established successful collaborations and creating the conditions for new ones, to enhance cooperation between France and Germany.