Xudong Zheng : Amplitude of Line Bundles and Fujita's Vanishing Theorem

Posted by Xudong Zheng , part of the Graduate Algebraic Geometry Seminar.

At

Feb. 24, 2014, 4 p.m.

In

SEO 712

Abstract

This talk continues on Section 1.4 of <i>Positivity, vol I</i>. Specifically, we shall discuss Kleiman's numerical criterion of ampleness of $\mathbb{R}$-divisors in terms of cones in the Néron-Severi space and its dual space of numerical classes of one cycles of the variety. In the second part, we introduce Fujita's vanishing theorem and some applications. In particular, we show that the numerically trivial line bundles form a bounded family for a projective variety.