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Proceedings of the Steklov Institute of Mathematics

, Volume 267, Issue 1, pp 235–247 | Cite as

Singularities of algebraic subvarieties and problems of birational geometry

  • A. V. Pukhlikov
Article

Abstract

We consider the connection between the problem of estimating the multiplicity of an algebraic subvariety at a given singular point and the problem of describing birational maps of rationally connected varieties. We describe the method of hypertangent divisors which makes it possible to give bounds for the multiplicities of singular points. The concept of birational rigidity of algebraic varieties is discussed.

Keywords

STEKLOV Institute Complete Intersection Fano Variety Cyclic Cover Birational Geometry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  1. 1.Steklov Institute of MathematicsRussian Academy of SciencesMoscowRussia
  2. 2.University of LiverpoolLiverpoolUK

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