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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
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
Citation:
V. Batyrev, F. Haddad, “On the Geometry of $\operatorname{SL}(2)$-Equivariant Flips”, Mosc. Math. J., 8:4 (2008), 621–646
Linking options:
https://www.mathnet.ru/eng/mmj323 https://www.mathnet.ru/eng/mmj/v8/i4/p621
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Abstract page: | 307 | Full-text PDF : | 3 | References: | 58 |
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