Half-canonical series on algebraic curves

Teixidor i Bigas, Montserrat

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

Half-canonical series on algebraic curves
HTML articles powered by AMS MathViewer

by Montserrat Teixidor i Bigas PDF

Trans. Amer. Math. Soc. 302 (1987), 99-115 Request permission

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.

References

Robert D. M. Accola, Plane models for Riemann surfaces admitting certain half-canonical linear series. I, Riemann surfaces and related topics: Proceedings of the 1978 Stony Brook Conference (State Univ. New York, Stony Brook, N.Y., 1978) Ann. of Math. Stud., vol. 97, Princeton Univ. Press, Princeton, N.J., 1981, pp. 7–20. MR 624801
Enrico Arbarello and Maurizio Cornalba, On a conjecture of Petri, Comment. Math. Helv. 56 (1981), no. 1, 1–38 (Italian). MR 615613, DOI 10.1007/BF02566195
Enrico Arbarello and Maurizio Cornalba, Footnotes to a paper of Beniamino Segre: “On the modules of polygonal curves and on a complement to the Riemann existence theorem” (Italian) [Math. Ann. 100 (1928), 537–551; Jbuch 54, 685], Math. Ann. 256 (1981), no. 3, 341–362. MR 626954, DOI 10.1007/BF01679702

A few remarks about the variety of irreducible plane curves of given degree and genus

16

Arnaud Beauville, Prym varieties and the Schottky problem, Invent. Math. 41 (1977), no. 2, 149–196. MR 572974, DOI 10.1007/BF01418373
Steven Diaz, Tangent spaces in moduli via deformations with applications to Weierstrass points, Duke Math. J. 51 (1984), no. 4, 905–922. MR 771387, DOI 10.1215/S0012-7094-84-05140-8
Hershel M. Farkas, Special divisors and analytic subloci of Teichmueller space, Amer. J. Math. 88 (1966), 881–901. MR 213546, DOI 10.2307/2373086
Joe Harris, Theta-characteristics on algebraic curves, Trans. Amer. Math. Soc. 271 (1982), no. 2, 611–638. MR 654853, DOI 10.1090/S0002-9947-1982-0654853-6
Eiji Horikawa, On deformations of holomorphic maps. I, J. Math. Soc. Japan 25 (1973), 372–396. MR 322209, DOI 10.2969/jmsj/02530372
Herbert Lange, Kurven mit rationaler Abbildung, J. Reine Angew. Math. 295 (1977), 80–115 (German). MR 476754, DOI 10.1515/crll.1977.295.80
David Mumford, Theta characteristics of an algebraic curve, Ann. Sci. École Norm. Sup. (4) 4 (1971), 181–192. MR 292836