Moduli space of semiorthogonal decompositions

Abstract: Semiorthogonal decomposition (SOD) of triangulated categories is quite interesting and of fundamental importance for various reasons. For example, SOD of the derived category of coherent sheaves is closely related to the geometry of varieties, such as the minimal model program (MMP) among others. It is therefore desirable to understand the general properties of SODs, partly so as to classify SODs of as many triangulated categories as possible. The purpose of this talk is to explain certain moduli spaces of SODs which we introduced. To a smooth projective morphism of excellent schemes f: X \to B, we associate an algebraic space over B which classifies the SODs of the derived categories of the fibers of f. We will discuss properties and various aspects of this moduli space including applications, comparison to MMP, and open problems.

algebraic geometry

Audience: researchers in the topic

ZAG (Zoom Algebraic Geometry) seminar

Series comments: Description: ZAG seminar

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