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arXiv · 1010.3377

Birational Contractions of $\bar{M}_{3,1}$ and $\bar{M}_{4,1}$

David Jensen
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Abstract

We study the birational geometry of $\bar{M}_{3,1}$ and $\bar{M}_{4,1}$. 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. 2010-10-16. Birational Contractions of $\bar{M}_{3,1}$ and $\bar{M}_{4,1}$. https://arxiv.org/abs/1010.3377

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