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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

   

 

Subcanonical points on algebraic curves


Author: Evan M. Bullock
Journal: Trans. Amer. Math. Soc. 365 (2013), 99-122
MSC (2010): Primary 14H55
Published electronically: July 23, 2012
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Abstract: If $ C$ is a smooth, complete algebraic curve of genus $ g\geq 2$ over the complex numbers, a point $ p$ of $ C$ is subcanonical if $ K_C \cong \mathcal {O}_C\big ((2g-2)p\big )$. We study the locus $ \mathcal {G}_g\subseteq \mathcal {M}_{g,1}$ of pointed curves $ (C,p)$, where $ p$ is a subcanonical point of $ C$. Subcanonical points are Weierstrass points, and we study their associated Weierstrass gap sequences. In particular, we find the Weierstrass gap sequence at a general point of each component of $ \mathcal {G}_g$ and construct subcanonical points with other gap sequences as ramification points of certain cyclic covers and describe all possible gap sequences for $ g\leq 6$.


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Additional Information

Evan M. Bullock
Affiliation: Department of Mathematics, Rice University, Houston, Texas 77005

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05506-1
PII: S 0002-9947(2012)05506-1
Received by editor(s): May 3, 2010
Received by editor(s) in revised form: November 5, 2010
Published electronically: July 23, 2012
Article copyright: © Copyright 2012 Evan M. Bullock