Existence of good divisors on Mukai varieties

TL;DR

This paper classifies Mukai varieties with log terminal singularities based on the existence of good divisors, providing new insights and a shorter proof of Mukai's conjecture.

Contribution

It offers a complete classification of log terminal Mukai varieties lacking good divisors and presents a shorter proof of Mukai's conjecture.

Findings

Identified conditions for the existence of good divisors on Mukai varieties

Classified all log terminal Mukai varieties without good divisors

Provided a shorter proof of Mukai Conjecture

Abstract

A Mukai variety is a Fano n-fold of index n-2. In this paper we study the fundamental divisor of a Mukai variety with at worst log terminal singularities. The main result is a complete classification of log terminal Mukai varieties which have not good divisors, examples of "bad" varieties are given. In such a way we also give a shorter proof of Mukai Conjecture, solved in our previous paper alg-geom/9611024.