On singular Fano varieties with a divisor of Picard number one

TL;DR

This paper investigates the geometric properties of mildly singular Fano varieties with a prime divisor of Picard number one, explores the case of toric varieties, and examines the lifting of extremal contractions to universal covers.

Contribution

It provides new insights into the structure of such Fano varieties, especially in relation to their singularities, toric cases, and universal coverings.

Findings

Characterization of mildly singular Fano varieties with specific divisors

Analysis of toric Fano varieties with similar properties

Results on lifting extremal contractions to universal covers

Abstract

In this paper we study the geometry of mildly singular Fano varieties on which there is an effective prime divisor of Picard number one. Afterwards, we address the case of toric varieties. Finally, we treat the lifting of extremal contractions to universal covering spaces in codimension 1.