Anticanonical divisors on Fano fourfolds

TL;DR

This paper proves that general anticanonical divisors on Fano fourfolds have at most terminal singularities and provides explicit local descriptions of these singularities.

Contribution

It establishes the nature of singularities on general anticanonical divisors of Fano fourfolds and characterizes their local structure.

Findings

General elements of |-K_X| have at most terminal singularities

Explicit local expressions for these singular points are provided

Contributes to understanding the geometry of Fano fourfolds

Abstract

In this paper we show that a general element of $|-K_X|$ on a four-dimensional Fano manifold has at most terminal singularities. We then determine an explicit local expression of these singular points.