Factorization Theorem for Projective Varieties with Finite Quotient Singularities

2005/02/22 by Yi Hu
Mathematics · #math.AG #math.DG

paper · pdf

published as J. Differential Geometry, 68 (2004), 587-593

arxiv created 2005/02/22 · arxiv updated 2009/12/01

Abstract

In this paper, we prove that any two birational projective varieties with finite quotient singularities can be realized as two geometric GIT quotients of a non-singular projective variety by a reductive algebraic group. Then, by applying the theory of Variation of Geometric Invariant Theory Quotients ([3]), we show that they are related by a sequence of GIT wall-crossing flips.

Related

• The birational geometry of GIT quotients
• Geometric Invariant Theory and Birational Geometry
• Geometric invariant theory and projective toric varieties
• Variation of Geometric Invariant Theory Quotients
• Computation of GIT quotients of semisimple groups