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Mosc. Math. J., 2008, Volume 8, Number 4, Pages 621–646 (Mi mmj323)  

This article is cited in 3 scientific papers (total in 3 papers)

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

V. Batyrev, F. Haddad

Mathematisches Institut, Universität Tübingen

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.

Full text: http://www.ams.org/.../abst8-4-2008.html
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Received: March 18, 2008
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
\mathnet{http://mi.mathnet.ru/mmj323}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2499357}
\zmath{https://zbmath.org/?q=an:05518635}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000261829900002}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. I. V. Arzhantsev, S. A. Gaifullin, “Cox rings, semigroups and automorphisms of affine algebraic varieties”, Sb. Math., 201:1 (2010), 1–21  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. Arzhantsev I., Liendo A., “Polyhedral Divisors and Sl2-Actions on Affine T-Varieties”, Mich. Math. J., 61:4 (2012), 731–762  crossref  mathscinet  zmath  isi  elib  scopus
    3. Arzhantsev I., Flenner H., Kaliman S., Kutzschebauch F., Zaidenberg M., “Flexible Varieties and Automorphism Groups”, Duke Math. J., 162:4 (2013), 767–823  crossref  mathscinet  zmath  isi  elib  scopus
  • Moscow Mathematical Journal
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