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Transactions of the American Mathematical Society

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

 

 

Half-canonical series on algebraic curves


Author: Montserrat Teixidor i Bigas
Journal: Trans. Amer. Math. Soc. 302 (1987), 99-115
MSC: Primary 14H10
DOI: https://doi.org/10.1090/S0002-9947-1987-0887499-X
MathSciNet review: 887499
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Abstract: Denote by $ \mathcal{M}_g^r$ the locus in the moduli space of curves of genus $ g$ of those curves which have a theta-characteristic of (projective) dimension at least $ r$. We give an upper bound for the dimension of $ \mathcal{M}_g^r$ and we determine this dimension completely for $ r \leqslant 4$. For $ r \leqslant 4$, we prove also that a generic point in every component of $ \mathcal{M}_g^r$ has a single theta-characteristic of this dimension.


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DOI: https://doi.org/10.1090/S0002-9947-1987-0887499-X
Keywords: Theta-characteristic
Article copyright: © Copyright 1987 American Mathematical Society