Fano threefolds

TL;DR

This paper provides a comprehensive modern overview of the classification of Fano threefolds, presenting a self-contained treatment suitable for researchers and students interested in algebraic geometry.

Contribution

It offers a unified, self-consistent presentation of the classification theory of Fano threefolds, integrating recent developments and perspectives.

Findings

Classification framework for Fano threefolds presented

Connections to modern algebraic geometry topics discussed

Published in both Russian and English editions

Abstract

The goal of these lecture notes is to present the modern point of view on the classification of Fano threefolds. We tried to offer a self-consistent treatment of the topics covered. \par\medskip\noindent These notes have been published in two versions: a Russian edition in \textit{Lektsionnye Kursy NOTs} \textbf{31}. Steklov Inst. Math., Moscow (ISBN 978-5-98419-085-5), doi: \href{https://doi.org/10.4213/lkn31}{10.4213/book1907}, and an English translation in the \textit{Proc. Steklov Inst. Math.}, \textbf{328}, Suppl. 1 (2025), doi: \href{https://doi.org/10.1134/S0081543825020014}{10.1134/S0081543825020014}