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

作者：Alper Jarod^*; Fedorchuk Maksym; Smyth David Ishii

来源：Compositio Mathematica, 2017, 153(8): 1584-1609.

DOI：10.1112/S0010437X16008289

• algebraic stacks
• good moduli spaces
• Hassett-Keel program

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 (M) over bar (g,n) (alpha) parameterizing alpha-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.

• 出版日期2017-8