Derived categories and birational geometry
Release Date： 2025-10-17 Unit： Department of Mathematics
Professor：Dr. Pedro Núñez (National Taiwan University)
Theme：Derived categories and birational geometry
Date：Oct. 23th (Thu) 15:30 ~ 17:00
Location：Hong-Jing Building, M107
Abstract：
Birational geometry aims at classifying projective varieties according to certain invariants, and derived categories are a convenient framework to compute such invariants. At the heart of modern birational geometry lies the Minimal Model Program: a quasi algorithmic process that performs a series of basic operations on any given projective variety and produces a relatively simple representative of its birational equivalence class (a minimal variety). These operations induce semiorthogonal decompositions in the derived category. And conversely, it is expected that most derived categories of minimal varieties do not admit any semiorthogonal decomposition. In this talk, we will introduce some of these concepts and present some recent progress in the direction of this indecomposability conjecture. The results are based on joint work with Pieter Belmans and Andreas Demleitner, and joint work in progress with Jungkai Alfred Chen.
Theme：Derived categories and birational geometry
Date：Oct. 23th (Thu) 15:30 ~ 17:00
Location：Hong-Jing Building, M107
Abstract：
Birational geometry aims at classifying projective varieties according to certain invariants, and derived categories are a convenient framework to compute such invariants. At the heart of modern birational geometry lies the Minimal Model Program: a quasi algorithmic process that performs a series of basic operations on any given projective variety and produces a relatively simple representative of its birational equivalence class (a minimal variety). These operations induce semiorthogonal decompositions in the derived category. And conversely, it is expected that most derived categories of minimal varieties do not admit any semiorthogonal decomposition. In this talk, we will introduce some of these concepts and present some recent progress in the direction of this indecomposability conjecture. The results are based on joint work with Pieter Belmans and Andreas Demleitner, and joint work in progress with Jungkai Alfred Chen.
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Updated: 2025-10-17
Category: Speech
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