Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Birational contractions of $ \overline{M}_{3,1}$ and $ \overline{M}_{4,1}$

Author: David Jensen
Journal: Trans. Amer. Math. Soc. 365 (2013), 2863-2879
MSC (2010): Primary 14H10, 14E30
Published electronically: November 27, 2012
MathSciNet review: 3034451
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Abstract: We study the birational geometry of $ \overline {M}_{3,1}$ and $ \overline {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.

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David Jensen
Affiliation: Department of Mathematics, Stony Brook University, Stony Brook, New York 11794

Received by editor(s): October 19, 2010
Received by editor(s) in revised form: February 3, 2011, and March 6, 2011
Published electronically: November 27, 2012
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.