A generalized non-vanishing theorem on surfaces
Algebraic Geometry
2024-10-22 v1
Abstract
We show that the anti-canonical bundle of any -factorial surface is numerically effective if and only if it is pseudo-effective. To prove this, we establish a numerical non-vanishing theorem for surfaces polarized with pseudo-effective divisors. The latter answers a question of C. Fontanari.
Cite
@article{arxiv.2410.15457,
title = {A generalized non-vanishing theorem on surfaces},
author = {Jihao Liu and Lingyao Xie},
journal= {arXiv preprint arXiv:2410.15457},
year = {2024}
}
Comments
7 pages. Final version, to appear in Pure and Applied Mathematics Quarterly (special volume in honor of Caucher Birkar)