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 Tr. Mat. Inst. Steklova, 2009, Volume 267, Pages 245–257 (Mi tm2607)

Singularities of Algebraic Subvarieties and Problems of Birational Geometry

A. V. Pukhlikovab

a Steklov Institute of Mathematics, Russian Academy of Sciences, Moscow, Russia
b University of Liverpool, Liverpool, United Kingdom

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.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2009, 267, 235–247

Bibliographic databases:

UDC: 512.7

Citation: A. V. Pukhlikov, “Singularities of Algebraic Subvarieties and Problems of Birational Geometry”, Singularities and applications, Collected papers, Tr. Mat. Inst. Steklova, 267, MAIK Nauka/Interperiodica, Moscow, 2009, 245–257; Proc. Steklov Inst. Math., 267 (2009), 235–247

Citation in format AMSBIB
\Bibitem{Puk09} \by A.~V.~Pukhlikov \paper Singularities of Algebraic Subvarieties and Problems of Birational Geometry \inbook Singularities and applications \bookinfo Collected papers \serial Tr. Mat. Inst. Steklova \yr 2009 \vol 267 \pages 245--257 \publ MAIK Nauka/Interperiodica \publaddr Moscow \mathnet{http://mi.mathnet.ru/tm2607} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2723954} \zmath{https://zbmath.org/?q=an:1223.14015} \elib{http://elibrary.ru/item.asp?id=12989377} \transl \jour Proc. Steklov Inst. Math. \yr 2009 \vol 267 \pages 235--247 \crossref{https://doi.org/10.1134/S0081543809040191} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000274252700019} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-76049089072}