[演講公告] Derived categories and birational geometry
發布日期： 2025-10-17 公告單位： 數學系
主 講 人：Pedro Núñez 紐培卓博士 (台大數學系博士後研究員)
演講題目：Derived categories and birational geometry
演講時間：2025年10月23日(星期四) 3:30 p.m. ~ 5:00 p.m.
演講地點：中央大學鴻經館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.
演講題目：Derived categories and birational geometry
演講時間：2025年10月23日(星期四) 3:30 p.m. ~ 5:00 p.m.
演講地點：中央大學鴻經館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.
更新日期: 2025-10-17
公告類別: 演講
瀏覽人次: 409