Geometric Invariant Theory and Birational Geometry

Details Geometric Invariant Theory and Birational Geometry Geometric Invariant Theory and Birational Geometry

2005-02-22

arxiv.org/abs/math/0502462v3

Mathematics

Algebraic Geometry

22 pages

Scientific paper

In this paper we will survey some recent developments in the last decade or so on variation of Geometric Invariant Theory and its applications to Birational Geometry such as the weak Factorization Theorems of nonsingular projective varieties and more generally projective varieties with finite quotient singularities. Along the way, we will also mention some progresses on birational geometry of hyperK\"ahler manifolds as well as certain open problems and conjectures.

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