Vol. 12, No. 8, 2018

Download this article
Download this article For screen
For printing
Recent Issues

Volume 18
Issue 10, 1767–1943
Issue 9, 1589–1766
Issue 8, 1403–1587
Issue 7, 1221–1401
Issue 6, 1039–1219
Issue 5, 847–1038
Issue 4, 631–846
Issue 3, 409–629
Issue 2, 209–408
Issue 1, 1–208

Volume 17, 12 issues

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN 1944-7833 (online)
ISSN 1937-0652 (print)
 
Author index
To appear
 
Other MSP journals
On nonprimitive Weierstrass points

Nathan Pflueger

Vol. 12 (2018), No. 8, 1923–1947
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.

Keywords
Weierstrass points, numerical semigroups, algebraic curves, limit linear series
Mathematical Subject Classification 2010
Primary: 14H55
Milestones
Received: 2 September 2016
Revised: 5 January 2018
Accepted: 10 March 2018
Published: 4 December 2018
Authors
Nathan Pflueger
Department of Mathematics and Statistics
Amherst College
Amherst, MA
United States