Birationally solid Fano 3-fold hypersurfaces

Abstract

A Fano variety of Picard number $1$ is said to be \textit{birationally solid} if it is not birational to a Mori fiber space over a positive dimensional base. In this paper we complete the classification of quasi-smooth birationally solid Fano $3$-fold weighted hypersurfaces.

arXiv comment72 pages. v3: Introduction is slightly modified and a reference is added. v2: A short section (Section 2.1.3) discussing the classification of Fano 3-fold weighted hypersurfaces is added, and some typos are corrected