# Canonical and log canonical thresholds of Fano complete intersections

## TL;DR

This paper proves that generic Fano complete intersections of certain dimensions and degrees have a log canonical threshold of one, leading to the existence of Kähler-Einstein metrics on these varieties.

## Contribution

It establishes the exact value of the global log canonical threshold for a broad class of Fano complete intersections, improving previous bounds and results.

## Key findings

- Global log canonical threshold equals one for specified Fano complete intersections
- Existence of Kähler-Einstein metrics on generic Fano complete intersections
- Improved bounds over previous results

## Abstract

It is proved that the global log canonical threshold of a Zariski general Fano complete intersection of index 1 and codimension $k$ in ${\mathbb P}^{M+k}$ is equal to one, if $M\geqslant 2k+3$ and the maximum of the degrees of defining equations is at least 8. This is an essential improvements of the previous results about log canonical thresholds of Fano complete intersections. As a corollary we obtain the existence of K\" ahler-Einstein metrics on generic Fano complete intersections described above.