English

On the geometry of SL(2)-equivariant flips

Algebraic Geometry 2008-03-18 v1 Combinatorics

Abstract

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.

Keywords

Cite

@article{arxiv.0803.2504,
  title  = {On the geometry of SL(2)-equivariant flips},
  author = {Victor Batyrev and Fatima Haddad},
  journal= {arXiv preprint arXiv:0803.2504},
  year   = {2008}
}

Comments

26 pages

R2 v1 2026-06-21T10:22:13.126Z