Seminario di algebra e geometria
ore
09:30
presso Aula Enriques
Mukai found the relation between polarized symplectic
automorphism groups and certain subgroups of the Mathieu group.
After the discovery of Mathieu moonshine, Huybrechts established the
relation between autoequivalence groups of derived categories of K3
surfaces and certain subgroups of the Conway group. Although we know
explicit examples of polarized K3 surfaces with maximal symplectic
automorphism groups, it is difficult to find explicit examples of finite
autoequivalences of derived categories of K3 surfaces not conjugate to
automorphisms of K3 surfaces.
In this talk, I would like to study how to construct finite
autoequivalences of derived categories of K3 surfaces and discuss their
difficulties.
First, we recall automorphism groups of compact Riemann surfaces from
point of view of algebraic geometry, topology and derived categories.
Second, I would like to discuss autoequivalence groups of derived
categories of K3 surfaces as an analogue of the case of compact Riemann
surfaces.