# Anticanonical system of Fano fivefolds

## TL;DR

This paper proves the existence and properties of anticanonical divisors on Fano fivefolds with certain singularities, including their effectiveness, reducedness, and singularity types, advancing understanding of their geometric structure.

## Contribution

It establishes the nonvanishing and singularity properties of the anticanonical system for Fano fivefolds with Gorenstein singularities, extending known results to higher dimensions.

## Key findings

- Any Fano fivefold with canonical Gorenstein singularities has an effective anticanonical divisor.
- A general element of the anticanonical system can be reduced and has canonical singularities.
- Nonvanishing of the anticanonical system is proven for log canonical Gorenstein singularities.

## Abstract

We show that any Fano fivefold with canonical Gorenstein singularities has an effective anticanonical divisor. Moreover,if a general element of the anticanonical system is reduced, then it has canonical singularities. We also prove nonvanishing of anticanonical system in the case of log canonical Gorenstein singularities.