Half-canonical series on algebraic curves

Teixidor i Bigas, Montserrat

doi:10.1090/S0002-9947-1987-0887499-X

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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
MathSciNet review: 887499
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Abstract: Denote by $\mathcal{M}_g^r$ the locus in the moduli space of curves of genus of those curves which have a theta-characteristic of (projective) dimension at least . 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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