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Extremal higher codimension cycles on moduli spaces of curves.

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journal contribution
posted on 28.01.2016, 00:00 by D Chen, I Coskin
We show that certain geometrically defined higher codimension cycles are extremal in the effective cone of the moduli space Mg,n of stable genus g curves with n ordered marked points. In particular, we prove that codimension two boundary strata are extremal and exhibit extremal boundary strata of higher codimension. We also show that the locus of hyperelliptic curves with a marked Weierstrass point in M3,1 and the locus of hyperelliptic curves in M4 are extremal cycles. In addition, we exhibit infinitely many extremal codimension two cycles in M1,n for n ≥ 5 and in M2,n for n ≥ 2.

Funding

The first author was partially supported by the NSF grant DMS-1200329, the NSF CAREER grant DMS-1350396, and the second author was partially supported by the NSF CAREER grant DMS-0950951535.

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Publisher Statement

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Proceedings of the London Mathematical Society following peer review. The definitive publisher-authenticated version Chen, D. and Coskun, I. Extremal higher codimension cycles on moduli spaces of curves. Proceedings of the London Mathematical Society. 2015. 111(1): 181-204. 10.1112/plms/pdv029, is available online at: http://plms.oxfordjournals.org/content/111/1/181

Publisher

London Mathematical Society

issn

0024-6115

Issue date

01/01/2015

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