# Geometric invariant theory and flips

@article{Thaddeus1994GeometricIT, title={Geometric invariant theory and flips}, author={Michael Thaddeus}, journal={Journal of the American Mathematical Society}, year={1994}, volume={9}, pages={691-723} }

We study the dependence of geometric invariant theory quotients on the choice of a linearization. We show that, in good cases, two such quotients are related by a flip in the sense of Mori, and explain the relationship with the minimal model programme. Moreover, we express the flip as the blow-up and blow-down of specific ideal sheaves, leading, under certain hypotheses, to a quite explicit description of the flip. We apply these ideas to various familiar moduli problems, recovering results of…

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