Title of Seminar: Algebraic Geometry Preprint Seminar 2025
Title of Talk: Non vanishing implies numerical dimension one abundance
Speaker: Swapnajit Das, TIFR, Mumbai
Date: November 11, 2025
Time: 16:00:00 Hours
Venue: AG-77

Abstract: The Abundance Conjecture predicts that the Kodaira dimension of a smooth projective variety equals its numerical Kodaira dimension. It is known in dimension three by the work of Kawamata and Miyaoka. Recently, Jihao Liu and Zheng Xu proved abundance in dimension at most five when the numerical dimension is one and the Kodaira dimension is zero, and more generally showed that non-vanishing implies abundance for log canonical pairs of numerical dimension one. In this talk, I will outline the main ideas of their proof and mention some applications.{\tt This talk is based on https://arxiv.org/abs/2505.05250v2.}