Algebra & Number Theory

On nonprimitive Weierstrass points

Nathan Pflueger

Abstract

We give an upper bound for the codimension in $ℳg,1$ of the variety $ℳG,1S$ 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 $ℳG,1S$ 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 $ℳG,1S$ 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
Revised: 5 January 2018
Accepted: 10 March 2018
First available in Project Euclid: 21 December 2018

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

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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