Birational contractions of M 3,1 and M4,1

David Jensen

doi:10.1090/S0002-9947-2012-05581-4

Birational contractions of M _3,1 and M_4,1

David Jensen

Mathematics

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

6 Scopus citations

Abstract

We study the birational geometry of M_3,1 and M_4,1. In particular, we pose a pointed analogue of the Slope Conjecture and prove it in these low-genus cases. Using variation of GIT, we construct birational contractions of these spaces in which certain divisors of interest - the pointed Brill-Noether divisors - are contracted. As a consequence, we see that these pointed Brill- Noether divisors generate extremal rays of the effective cones for these spaces.

Original language	English
Pages (from-to)	2863-2879
Number of pages	17
Journal	Transactions of the American Mathematical Society
Volume	365
Issue number	6
DOIs	https://doi.org/10.1090/S0002-9947-2012-05581-4
State	Published - 2013

ASJC Scopus subject areas

Mathematics (all)
Applied Mathematics

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10.1090/S0002-9947-2012-05581-4

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abstract = "We study the birational geometry of M3,1 and M4,1. In particular, we pose a pointed analogue of the Slope Conjecture and prove it in these low-genus cases. Using variation of GIT, we construct birational contractions of these spaces in which certain divisors of interest - the pointed Brill-Noether divisors - are contracted. As a consequence, we see that these pointed Brill- Noether divisors generate extremal rays of the effective cones for these spaces.",

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Birational contractions of M _3,1 and M_4,1

Abstract

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