Fano fourfolds with large anticanonical base locus
Algebraic Geometry
2025-04-16 v2
Abstract
A famous theorem of Shokurov states that a general anticanonical divisor of a smooth Fano threefold is a smooth K3 surface. This is quite surprising since there are several examples where the base locus of the anticanonical system has codimension two. In this paper we show that for four-dimensional Fano manifolds the behaviour is completely opposite: if the base locus is a normal surface, hence has codimension two, all the anticanonical divisors are singular.
Keywords
Cite
@article{arxiv.2309.17029,
title = {Fano fourfolds with large anticanonical base locus},
author = {Andreas Höring and Saverio Andrea Secci},
journal= {arXiv preprint arXiv:2309.17029},
year = {2025}
}
Comments
Final version, 26 pages