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2018 On nonprimitive Weierstrass points
Nathan Pflueger
Algebra Number Theory 12(8): 1923-1947 (2018). DOI: 10.2140/ant.2018.12.1923


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.


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Nathan Pflueger. "On nonprimitive Weierstrass points." Algebra Number Theory 12 (8) 1923 - 1947, 2018.


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

zbMATH: 06999398
MathSciNet: MR3892968
Digital Object Identifier: 10.2140/ant.2018.12.1923

Primary: 14H55

Keywords: algebraic curves , limit linear series , numerical semigroups , Weierstrass points

Rights: Copyright © 2018 Mathematical Sciences Publishers


Vol.12 • No. 8 • 2018
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