Back to Algebraic Geometry Seminar: Fall 2025
Algebraic Geometry Seminar
Date: Tuesday, Sep 16, 2025
Time: 3:30PM - 4:30PM
Location: LCB 323
Daigo Ito
UC Berkeley
Title |
A derived category analogue of the Nakai--Moishezon criterion |
Abstract |
In the study of derived categories of coherent sheaves, ample line bundles play a fundamental role – their tensor powers generate the derived category. This raises a natural question: does this generation property characterize ampleness? The answer is negative, but we show that this categorical property can be checked by a classical numerical criterion naturally extending the Nakai–Moishezon criterion. Moreover, the cone of divisors satisfying this condition lies between the big cone and the ample cone. In this talk I will focus on explaining the case of surfaces, where the geometry becomes especially clear. This is a joint work with Noah Olander. |
Algebraic Geometry