Abstract
In this paper we give an explicit construction of the moduli space of the pointed complete Gorenstein curves of arithmetic genus g with a given quasi-symmetric Weierstrass semigroup, that is, a Weierstrass semigroup whose last gap is equal to 2g − 2. We identify such a curve with its image under the canonical embedding in the (g − 1)-dimensional projective space. By normalizing the coefficients of the quadratic relations and by constructing Gröbner bases of the canonical ideal, we obtain the equations of the moduli space in terms of Buchberger's criterion. Moreover, by analyzing syzygies of the canonical ideal we establish criteria that make the computations less expensive.
Similar content being viewed by others
References
Arbarello, E., Cornalba, M., Griffiths, P. A. and Harris, J.: Geometry of Algebraic Curves, vol. I, Springer, Berlin, Heidelberg, New York, 1985.
Oliveira, G.: Weierstrass semigroups and the canonical ideal of non-trigonal curves, Manuscripta Math. 71 (1991), 431–450.
Oliveira, G. and St ¨ ohr, K.-O.: Gorenstein curves with quasi-symmetric Weierstrass semigroups, Geom. Dedicata 67 (1997), 45–63.
Petri, K.: ¨ Uber die invariante Darstellung algebraischer Funktionen einer Ver¨ anderlichen, Math. Ann. 88 (1923), 242–289.
Pinkham, H.: Deformations of algebraic varieties with G m-action, Ast´ erisque 20 (1974).
Rathmann, J.: The uniform position principle for curves in characteristic p, Math. Ann. 276 (1987), 565–579.
Schreyer, F. O.: A standard basis approach to syzygies of canonical curves, J. reine angew. Math. 421 (1991), 83–123.
St ¨ ohr, K.-O.: On the moduli spaces of Gorenstein curves with symmetric Weierstrass semigroups, J. reine angew. Math. 441 (1993), 189–213.
St ¨ ohr, K.-O. and Viana, P.: A variant of Petri's analysis of the canonical ideal of an algebraic curve, Manuscripta Math. 61 (1988), 223–248.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Oliveira, G., Stöhr, KO. Moduli Spaces of Curves with Quasi-Symmetric Weierstrass GAp Seqnences. Geometriae Dedicata 67, 65–82 (1997). https://doi.org/10.1023/A:1004943511841
Issue Date:
DOI: https://doi.org/10.1023/A:1004943511841