“Moduli spaces of semiorthogonal decompositions”
Martedì 2 Dicembre 2025, ore 14:30 - Aula 2AB45 - Andrea Ricolfi (SISSA, Trieste)
Abstract
The bounded derived category of coherent sheaves on a smooth projective variety X is a sensible and somewhat subtle invariant of X. Its study is tightly related to rationality problems, MMP, Mirror Symmetry, Enumerative Geometry. Semiorthogonal decompositions (SODs) are a gadget allowing one to “decompose” this category into smaller pieces. Proving the very existence of SODs is often a delicate question. In this talk we shall explain how to construct a “moduli space of SODs” attached to a smooth proper morphism of schemes; we will also discuss its main properties, and how to use it to detect indecomposability of derived categories of some smooth projective varieties. Joint work with Pieter Belmans and Shinnosuke Okawa.
