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Essentials of the method of maximal singularities

Aleksandr V. Pukhlikov
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Abstract

A consistent exposition of the arguments and constructions of the method of maximal singularities, the aim of which is to describe birational iso/automorphisms of Fano varieties and Fano fibrations. The principal elements of the method are considered: N{\" o}ther-Fano inequality, maximal cycles, infinitely near maximal singularities, exclusion and untwisting. In a detailed way the crucial technical points are discussed. We also give a new version of the proof of Sarkisov theorem which is ideologically more close to the original arguments of V.A.Iskovskikh and Yu.I.Manin.

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Aleksandr V. Pukhlikov. 1998-06-24. Essentials of the method of maximal singularities. https://arxiv.org/abs/math/9806138

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