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Moscow Mathematical Journal, 2008, Volume 8, Number 4, Pages 621–646
DOI: https://doi.org/10.17323/1609-4514-2008-8-4-621-646
(Mi mmj323)
 

This article is cited in 8 scientific papers (total in 8 papers)

On the Geometry of $\operatorname{SL}(2)$-Equivariant Flips

V. Batyrev, F. Haddad

Mathematisches Institut, Universität Tübingen
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Abstract: In this paper, we show that any 3-dimensional normal affine quasihomogeneous $\operatorname{SL}(2)$-variety can be described as a categorical quotient of a 4-dimensional affine hypersurface. Moreover, we show that the Cox ring of an arbitrary 3-dimensional normal affine quasihomogeneous $\operatorname{SL}(2)$-variety has a unique defining equation. This allows us to construct $\operatorname{SL}(2)$-equivariant flips by different GIT-quotients of hypersurfaces. Using the theory of spherical varieties, we describe $\operatorname{SL}(2)$-flips by means of 2-dimensional colored cones.
Key words and phrases: geometric invariant theory, categorical quotient, Mori theory.
Received: March 18, 2008
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Language: English
Citation: V. Batyrev, F. Haddad, “On the Geometry of $\operatorname{SL}(2)$-Equivariant Flips”, Mosc. Math. J., 8:4 (2008), 621–646
Citation in format AMSBIB
\Bibitem{BatHad08}
\by V.~Batyrev, F.~Haddad
\paper On the Geometry of $\operatorname{SL}(2)$-Equivariant Flips
\jour Mosc. Math.~J.
\yr 2008
\vol 8
\issue 4
\pages 621--646
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\crossref{https://doi.org/10.17323/1609-4514-2008-8-4-621-646}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2499357}
\zmath{https://zbmath.org/?q=an:05518635}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000261829900002}
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  • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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