@article{thaddeus_geometric_1994,
	title = {Geometric invariant theory and flips},
	url = {https://arxiv.org/abs/alg-geom/9405004v1},
	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 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 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.},
	language = {en},
	urldate = {2019-06-28},
	author = {Thaddeus, Michael},
	month = may,
	year = {1994}
}

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