Fano varieties with $\mathrm{Nef}(X)=\mathrm{Psef}(X)$ and $\rho(X)=\mathrm{dim}\, X-1$

TL;DR

This paper classifies certain mildly singular Fano varieties where the nef and pseudo-effective cones coincide and the Picard number is one less than the dimension, advancing understanding of their geometric structure.

Contribution

It provides a classification of mildly singular Fano varieties with specific cone and Picard number conditions, a new result in algebraic geometry.

Findings

Classification of such Fano varieties achieved

Characterization of their geometric properties

Extension of known results to mildly singular cases

Abstract

We classify mildly singular Fano varieties $X$ such that $\mathrm{Nef}(X)=\mathrm{Psef}(X)$ and that the Picard number of $X$ is equal to the dimension of $X$ minus $1$.