English

Essentials of the method of maximal singularities

Algebraic Geometry 2007-05-23 v1

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.

Keywords

Cite

@article{arxiv.math/9806138,
  title  = {Essentials of the method of maximal singularities},
  author = {Aleksandr V. Pukhlikov},
  journal= {arXiv preprint arXiv:math/9806138},
  year   = {2007}
}

Comments

LATEX, 25 pages, to appear in "Proceedings of Symposium in Algebraic Geometry", ed. A.Corti and M.Reid. The volume is to come out in 1999

R2 v1 2026-07-22T17:59:05.188Z