Second flip in the Hassett–Keel program: Projectivity

Jarod Alper; Maksym Fedorchuk; David Ishii Smyth

doi:10.1093/imrn/rnw216

Second flip in the Hassett–Keel program: Projectivity

Jarod Alper, Maksym Fedorchuk^*, David Ishii Smyth

^*Corresponding author for this work

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

10 Citations (Scopus)

Abstract

For the moduli stacks of α-stable curves introduced in [4], we prove nefness of natural log canonical divisors, thus generalizing a well-known result of Cornalba and Harris for the moduli stack of Deligne–Mumford stable curves. We then deduce the projectivity of the good moduli spaces of α-stable curves and identify these moduli spaces with the log canonical models of M _g _,n appearing in the Hassett–Keel program.

Original language	English
Pages (from-to)	7375-7419
Number of pages	45
Journal	International Mathematics Research Notices
Volume	2017
Issue number	24
DOIs	https://doi.org/10.1093/imrn/rnw216
Publication status	Published - 1 Dec 2017

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10.1093/imrn/rnw216

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title = "Second flip in the Hassett–Keel program: Projectivity",

abstract = " For the moduli stacks of α-stable curves introduced in [4], we prove nefness of natural log canonical divisors, thus generalizing a well-known result of Cornalba and Harris for the moduli stack of Deligne–Mumford stable curves. We then deduce the projectivity of the good moduli spaces of α-stable curves and identify these moduli spaces with the log canonical models of M g ,n appearing in the Hassett–Keel program.",

author = "Jarod Alper and Maksym Fedorchuk and Smyth, \{David Ishii\}",

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AU - Alper, Jarod

AU - Fedorchuk, Maksym

AU - Smyth, David Ishii

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N2 - For the moduli stacks of α-stable curves introduced in [4], we prove nefness of natural log canonical divisors, thus generalizing a well-known result of Cornalba and Harris for the moduli stack of Deligne–Mumford stable curves. We then deduce the projectivity of the good moduli spaces of α-stable curves and identify these moduli spaces with the log canonical models of M g ,n appearing in the Hassett–Keel program.

AB - For the moduli stacks of α-stable curves introduced in [4], we prove nefness of natural log canonical divisors, thus generalizing a well-known result of Cornalba and Harris for the moduli stack of Deligne–Mumford stable curves. We then deduce the projectivity of the good moduli spaces of α-stable curves and identify these moduli spaces with the log canonical models of M g ,n appearing in the Hassett–Keel program.

UR - https://www.scopus.com/pages/publications/85019190490

U2 - 10.1093/imrn/rnw216

DO - 10.1093/imrn/rnw216

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VL - 2017

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EP - 7419

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 24

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Second flip in the Hassett–Keel program: Projectivity

Abstract

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