Shijie Shang : Seshadri Constants on Algebraic Surfaces

Posted by Gregory Taylor , part of the Graduate Algebraic Geometry Seminar.

At

Nov. 6, 2019, 5 p.m.

In

712 SEO

Abstract

The theory of Seshadri constants originates with Demailly's idea for quantifying how much of the positivity of an ample line bundle can be localized at a given point of a variety. First, I will talk about a theorem of Ein and Lazarsfeld, which gives a universal lower bound of Seshadri constants at a very general point of smooth complex projective surfaces. Then I will introduce Miranda's example, which illustrates that there cannot exist lower bounds on Seshadri constants holding at every point of every surface. At last, I will discuss a generalized version of Miranda's example constructed by Bauer.