Algebra & Number Theory
- Algebra Number Theory
- Volume 12, Number 8 (2018), 1923-1947.
On nonprimitive Weierstrass points
We give an upper bound for the codimension in of the variety of marked curves 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 , the variety 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 is known, as evidence that the effective weight estimate is correct in wider circumstances.
Algebra Number Theory, Volume 12, Number 8 (2018), 1923-1947.
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
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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