TY - JOUR
T1 - Birational contractions of M 3,1 and M4,1
AU - Jensen, David
N1 - Copyright:
Copyright 2013 Elsevier B.V., All rights reserved.
PY - 2013
Y1 - 2013
N2 - 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.
AB - 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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U2 - 10.1090/S0002-9947-2012-05581-4
DO - 10.1090/S0002-9947-2012-05581-4
M3 - Article
AN - SCOPUS:84875498874
SN - 0002-9947
VL - 365
SP - 2863
EP - 2879
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 6
ER -