Birational Contractions of $\bar{M}_{3,1}$ and $\bar{M}_{4,1}$
Algebraic Geometry
2011-02-09 v2
Abstract
We study the birational geometry of and . 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.
Keywords
Cite
@article{arxiv.1010.3377,
title = {Birational Contractions of $\bar{M}_{3,1}$ and $\bar{M}_{4,1}$},
author = {David Jensen},
journal= {arXiv preprint arXiv:1010.3377},
year = {2011}
}