Singularities of algebraic subvarieties and problems of birational geometry
type: Item
instance of: scholarly article
title: Singularities of algebraic subvarieties and problems of birational geometry
zbMATH Open document ID: 1223.14015
DOI: 10.1134/S0081543809040191
published in: Proceedings of the Steklov Institute of Mathematics
publication date: 2010-11-01T00:00:00Z
review text: The paper under review gives an account on how a method of estimating multiplicities of singularities on an algebraic variety can be applied to the problem of describing birational maps of rationally connected varieties. A variety is \textit{rationally connected} if any two general points on it can be joined by a rational curve. A method of hypertangent divisors is surveyed and it is demonstrated how to construct these divisors on complete intersections. Finally, it is shown how this implies, for instance, that generic hypersurfaces of degree \(d\) in the projective \(d\)-space are birationally superrigid.
Mathematics Subject Classification ID: 14E05
Mathematics Subject Classification ID: 14J17
Mathematics Subject Classification ID: 14E30
zbMATH DE Number: 5809085
zbMATH Keywords: multiplicities of singularities
zbMATH Keywords: birational rigidity
author: A. V. Pukhlikov
reviewed by: Vladimir Lazic
MaRDI profile type: Publication
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full work available at URL: s0081543809040191
OpenAlex ID: W2056128869
description: scientific article; zbMATH DE number 5809085