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Intersection Divisors of a Canonically Embedded Curve with its Osculating Spaces

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Abstract

We present a new result on the geometry of nonhyperelliptic curves; namely, the intersection divisors of a canonically embedded curve C with its osculating spaces at a point P, not considering the intersection at P, can only vary in dimensions given by the Weierstrass semigroup of the curve C at P. We obtain, under a reasonable geometrical hypothesis, monomial bases for the spaces of higher-order regular differentials. We also give a sufficient condition on the Weierstrass semigroup of C at P in order for this geometrical hypothesis to be true. Finally, we give examples of Weierstrass semigroups satisfying this condition.

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References

  • [K] Komeda, J.: On the existence of Weierstrass gaps sequences on curves of genus ⩽8, J. Pure Appl. Algebra 97 (1994), 51–71.

    Google Scholar 

  • [O] Oliveira, G.: Weierstrass semigroups and the canonical ideal of non-trigonal curves, Manuscripta Math. 71 (1991), 431–450.

    Google Scholar 

  • [OS1] Oliveira, G. and Stöhr, K.-O.: Gorenstein curves with quasi-symmetric Weierstrass semigroups, Geom. Dedicata 67 (1997), 45–63.

    Google Scholar 

  • [OS2] Oliveira, G. and Stöhr, K.-O.: Moduli Spaces of curves with quasi-symmetric Weierstrass gap sequences, Geom. Dedicata 67 (1997), 65–82.

    Google Scholar 

  • [S] Stöhr, K.-O.: On the moduli spaces of Gorenstein curves with symmetric Weiestrass semigroups, J. Reine Angew. Math. 441 (1993), 189–213.

    Google Scholar 

  • [SV] Stoöhr, K.-O. and Viana, P.: A variant of Petri's analysis of the canonical ideal of an algebraic curves, Manuscripta Math. 61 (1988), 223–248.

    Google Scholar 

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Authors and Affiliations

  1. Centro de Ciências, Coordenação da Pós-Graduação em Matemática, Bloco 914, Universidade Federal do Ceará, CEP 60455-750, Campus do Pici, Fortaleza, Ceará, Brasil

    Francisco Luis Rocha Pimentel

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  1. Francisco Luis Rocha Pimentel
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Pimentel, F.L.R. Intersection Divisors of a Canonically Embedded Curve with its Osculating Spaces. Geometriae Dedicata 85, 125–134 (2001). https://doi.org/10.1023/A:1010379403737

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  • DOI: https://doi.org/10.1023/A:1010379403737

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