Fano threefolds

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}

115 pages , LaTeX

References in corpus (9)

• Hilbert schemes of lines and conics and automorphism groups of Fano threefolds
• Simple finite subgroups of the Cremona group of rank 3
• Gushel--Mukai varieties: classification and birationalities
• The rationality problem for conic bundles
• Extremal contractions from 4-dimensional manifolds to 3-folds
• On nodal prime Fano threefolds of degree 10
• On the number of singular points of factorial terminal Fano threefolds
• Prime Fano threefolds of genus 12 with a $G_m$-action
• On the existence of good divisors on Fano varieties of coindex 3