Geometric invariant theory and flips

  title={Geometric invariant theory and flips},
  author={Michael Thaddeus},
  journal={Journal of the American Mathematical Society},
  • M. Thaddeus
  • Published 10 May 1994
  • Mathematics
  • Journal of the American Mathematical Society
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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