On the geometry of SL(2)-equivariant flips

Details On the geometry of SL(2)-equivariant flips On the geometry of SL(2)-equivariant flips

2008-03-17

arxiv.org/abs/0803.2504v1

Mathematics

Algebraic Geometry

26 pages

Scientific paper

In this paper, we show that any 3-dimensional normal affine quasihomogeneous 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 SL(2)-variety has a unique defining equation. This allows us to construct SL(2)-equivariant flips by different GIT-quotients of hypersurfaces. Using the theory of spherical varieties, we describe SL(2)-flips by means of 2-dimensional colored cones.

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