Mukai models of Fano varieties

TL;DR

This paper provides a simplified, self-contained proof of Mukai's classification of certain prime Fano varieties, extending the results to higher dimensions and focusing on those with specific singularities.

Contribution

It offers a new, streamlined proof of Mukai's classification for prime Fano threefolds and extends the classification to higher-dimensional cases.

Findings

Classification of prime Fano threefolds with specific singularities

Extension of Mukai's classification to higher dimensions

Simplified proof approach for Mukai's results

Abstract

We give a self-contained and simplified proof of Mukai's classification of prime Fano threefolds of index 1 and genus $g \ge 6$ with at most Gorenstein factorial terminal singularities, and of its extension to higher-dimension.