Algebra & Number Theory

On nonprimitive Weierstrass points

Nathan Pflueger

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Abstract

We give an upper bound for the codimension in g,1 of the variety G,1S of marked curves (C,p) with a given Weierstrass semigroup. The bound is a combinatorial quantity which we call the effective weight of the semigroup; it is a refinement of the weight of the semigroup, and differs from the weight precisely when the semigroup is not primitive. We prove that whenever the effective weight is less than g, the variety G,1S is nonempty and has a component of the predicted codimension. These results extend previous results of Eisenbud, Harris, and Komeda to the case of nonprimitive semigroups. We also survey other cases where the codimension of G,1S is known, as evidence that the effective weight estimate is correct in wider circumstances.

Article information

Source
Algebra Number Theory, Volume 12, Number 8 (2018), 1923-1947.

Dates
Received: 2 September 2016
Revised: 5 January 2018
Accepted: 10 March 2018
First available in Project Euclid: 21 December 2018

Permanent link to this document
https://projecteuclid.org/euclid.ant/1545361465

Digital Object Identifier
doi:10.2140/ant.2018.12.1923

Mathematical Reviews number (MathSciNet)
MR3892968

Zentralblatt MATH identifier
06999398

Subjects
Primary: 14H55: Riemann surfaces; Weierstrass points; gap sequences [See also 30Fxx]

Keywords
Weierstrass points numerical semigroups algebraic curves limit linear series

Citation

Pflueger, Nathan. On nonprimitive Weierstrass points. Algebra Number Theory 12 (2018), no. 8, 1923--1947. doi:10.2140/ant.2018.12.1923. https://projecteuclid.org/euclid.ant/1545361465


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