Project Details
Projekt
Positivity on K-trivial varieties
Applicants
Professor Dr. Daniele Agostini; Professor Dr. Alex Küronya; Professor Dr. Vladimir Lazic; Professor Dr. Christian Lehn
Subject Area
Mathematics
Term
since 2023
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 530132094
Varieties with trivial canonical bundle, also known as K-trivial varieties, possess an extremely rich geometry and continue to fascinate algebraic and complex geometers in many ways. In recent years, there have been major breakthroughs both in the theory itself (e.g. a generalization of the Beauville-Bogomolov decomposition theorem to the singular setting) and in related areas (e.g. birational geometry, analytic methods, Kähler-Einstein techniques, deformation theory) that have already been applied successfully to the study of K-trivial varieties. The goal of the project is to exploit these recent advances and apply various state-of-the-art techniques in order to attack several fundamental questions concerning K-trivial varieties, thus verifying in this framework general conjectures that guide the study of algebraic varieties. We focus more specifically on various positivity problems such as: (a) the study of linear systems on K-trivial varieties and their properties: base loci, abundance-conjecture-type problems, Fujita-conjecture type problems; (b) higher syzygies of K-trivial varieties: Mukai’s conjecture, geometric characterizations of property (Np); (c) the Kawamata-Morrison cone conjecture and applications to minimal models; (d) the detailed study of Newton-Okounkov bodies on K-trivial varieties and their applications.To achieve our goal, we bring together a group of researchers with different and complementary expertise We rely on well-established successful collaborations and at the same time we will create the conditions for new ones, enhancing cooperation between France and Germany.
DFG Programme
Research Grants
International Connection
France
