Second flip in the Hassett-Keel program: Existence of good moduli spaces

Jarod Alper; Maksym Fedorchuk; David Ishii Smyth

doi:10.1112/S0010437X16008289

Second flip in the Hassett-Keel program: Existence of good moduli spaces

Jarod Alper, Maksym Fedorchuk, David Ishii Smyth

Research output: Contribution to journal › Article › peer-review

21 Citations (Scopus)

Abstract

We prove a general criterion for an algebraic stack to admit a good moduli space. This result may be considered as a generalization of the Keel-Mori theorem, which guarantees the existence of a coarse moduli space for a separated Deligne-Mumford stack. We apply this result to prove that the moduli stacks parameterizing-stable curves introduced in [J. Alper et al., Second flip in the Hassett-Keel program: A local description, Compositio Math. 153 (2017), 1547-1583] admit good moduli spaces.

Original language	English
Pages (from-to)	1584-1609
Number of pages	26
Journal	Compositio Mathematica
Volume	153
Issue number	8
DOIs	https://doi.org/10.1112/S0010437X16008289
Publication status	Published - 1 Aug 2017

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abstract = "We prove a general criterion for an algebraic stack to admit a good moduli space. This result may be considered as a generalization of the Keel-Mori theorem, which guarantees the existence of a coarse moduli space for a separated Deligne-Mumford stack. We apply this result to prove that the moduli stacks parameterizing-stable curves introduced in [J. Alper et al., Second flip in the Hassett-Keel program: A local description, Compositio Math. 153 (2017), 1547-1583] admit good moduli spaces.",

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AU - Alper, Jarod

AU - Fedorchuk, Maksym

AU - Smyth, David Ishii

N1 - Publisher Copyright: © The Authors 2017.

PY - 2017/8/1

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N2 - We prove a general criterion for an algebraic stack to admit a good moduli space. This result may be considered as a generalization of the Keel-Mori theorem, which guarantees the existence of a coarse moduli space for a separated Deligne-Mumford stack. We apply this result to prove that the moduli stacks parameterizing-stable curves introduced in [J. Alper et al., Second flip in the Hassett-Keel program: A local description, Compositio Math. 153 (2017), 1547-1583] admit good moduli spaces.

AB - We prove a general criterion for an algebraic stack to admit a good moduli space. This result may be considered as a generalization of the Keel-Mori theorem, which guarantees the existence of a coarse moduli space for a separated Deligne-Mumford stack. We apply this result to prove that the moduli stacks parameterizing-stable curves introduced in [J. Alper et al., Second flip in the Hassett-Keel program: A local description, Compositio Math. 153 (2017), 1547-1583] admit good moduli spaces.

KW - Algebraic stacks

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JO - Compositio Mathematica

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ER -

Second flip in the Hassett-Keel program: Existence of good moduli spaces

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