Regeneration of Elliptic Chains with Exceptional Linear Series

Regeneration of Elliptic Chains with Exceptional Linear Series

We study two dimension estimates regarding linear series on algebraic curves. First, we generalize the classical Brill-Noether theorem to many cases where the Brill-Noether number is negative. Second, we extend results of Eisenbud, Harris, and Komeda on the existence of Weierstrass points with certa...

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Bibliographic Details
Main Author: Pflueger, Nathan K
Other Authors: Harris, Joseph D.
Language:en_US
Published: Harvard University 2014
Subjects:
Mathematics
algebraic curves
algebraic geometry
Brill-Noether theory
numerical semigroups
Weierstrass points
Online Access:http://dissertations.umi.com/gsas.harvard:11615
http://nrs.harvard.edu/urn-3:HUL.InstRepos:12274140
Description
Summary:We study two dimension estimates regarding linear series on algebraic curves. First, we generalize the classical Brill-Noether theorem to many cases where the Brill-Noether number is negative. Second, we extend results of Eisenbud, Harris, and Komeda on the existence of Weierstrass points with certain semigroups, by refining their dimension estimate in light of combinatorial considerations. Both results are proved by constructing chains of elliptic curves, joined at pairs of points differed by carefully chosen orders of torsion, and smoothing these chains. These arguments lead to several combinatorial problems of separate interest. === Mathematics

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