Gorenstein Curves with Quasi-Symmetric Weierstrass Semigroups View Full Text


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Article Info

DATE

1997-08

AUTHORS

Gilvan Oliveira, Karl-Lotto Stöhr

ABSTRACT

We consider a canonical Gorenstein curve C of arithmetic genus g in P g-1 (K), that admits a non-singular point P, whose Weierstrass semigroup is quasi-symmetric in the sense that the last gap is equal to 2g-2. By making local considerations at the point P and the second point of the curve C on its osculating hyperplane at P we construct monomial bases for the spaces of higher order regular differentials. We give an irreducibility criterion for the canonical curve in terms of the coefficients of the quadratic relations. We also realize each quasi-symmetric numerical semigroup as the Weierstrass semigroup of a reducible canonical Gorenstein curve, but we give examples of such semigroups that cannot be realized as Weierstrass semigroups of smooth curves. More... »

PAGES

45-63

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1023/a:1004995513658

DOI

http://dx.doi.org/10.1023/a:1004995513658

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1008053404


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