Rationality of Fano threefolds with terminal Gorenstein singularities, II

TL;DR

This paper classifies certain nonrational Fano threefolds with specific singularities, Picard rank, and divisor class group conditions, expanding understanding of their geometric properties.

Contribution

It provides a classification of nonrational Fano threefolds with terminal Gorenstein singularities under specified numerical and Picard group constraints.

Findings

Classification of nonrational Fano threefolds with given properties

Identification of conditions for rationality and nonrationality

Insights into the structure of Fano threefolds with terminal Gorenstein singularities

Abstract

We classify nonrational Fano threefolds $X$ with terminal Gorenstein singularities such that $\mathrm{\rk}\, \mathrm{\Pic}(X)=1$, $(-K_X)^3\ge 8$, and $\mathrm{\rk}\, \mathrm{\Cl}(X)\le 2$.