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Geometric invariant theory and flips
Author(s):
Michael
Thaddeus
Journal:
J. Amer. Math. Soc.
9
(1996),
691-723.
MSC (1991):
Primary 14L30, 14D20
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Abstract:
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 program. 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 Kirwan, Boden-Hu, Bertram-Daskalopoulos-Wentworth, and the author. Along the way we display a chamber structure, following Duistermaat-Heckman, on the space of all linearizations. We also give a new, easy proof of the Bialynicki-Birula decomposition theorem.
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Additional Information:
Michael
Thaddeus
Affiliation:
St. John's College, Oxford, England
Address at time of publication:
Department of Mathematics, Harvard University, 1 Oxford St., Cambridge, Massachusetts 02138
Email:
thaddeus@math.harvard.edu
DOI:
10.1090/S0894-0347-96-00204-4
PII:
S 0894-0347(96)00204-4
Received by editor(s):
November 11, 1994
Received by editor(s) in revised form:
March 23, 1995
Copyright of article:
Copyright
1996,
American Mathematical Society
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