Lifting divisors on a generic chain of loops

Dustin Cartwright; David Jensen; Sam Payne

doi:10.4153/CMB-2014-050-2

Lifting divisors on a generic chain of loops

Dustin Cartwright, David Jensen, Sam Payne

Mathematics

Research output: Contribution to journal › Article › peer-review

20 Scopus citations

Abstract

Let C be a curve over a complete valued field having an infinite residue field and whose skeleton is a chain of loops with generic edge lengths. We prove that any divisor on the chain of loops that is rational over the value group lifts to a divisor of the same rank on C, confirming a conjecture of Cools, Draisma, Robeva, and the third author.

Original language	English
Pages (from-to)	250-262
Number of pages	13
Journal	Canadian Mathematical Bulletin
Volume	58
Issue number	2
DOIs	https://doi.org/10.4153/CMB-2014-050-2
State	Published - Jun 2015

Bibliographical note

Publisher Copyright:
© Canadian Mathematical Society 2015.

Funding

The second author was supported in part by an AMS-Simons Travel Grant. The third author was supported in part by NSF DMS-1068689 and by NSF CAREER DMS-1149054.

Funders	Funder number
AMS-Simons
NSF DMS-1068689	DMS-1068689
NSF CAREER DMS-1149054	DMS-1149054
National Science Foundation Arctic Social Science Program	1068689, 1149054

Keywords

Brill-Noether theory
Special divisors on algebraic curves
Tropical geometry

ASJC Scopus subject areas

General Mathematics

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10.4153/CMB-2014-050-2

Cite this

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N2 - Let C be a curve over a complete valued field having an infinite residue field and whose skeleton is a chain of loops with generic edge lengths. We prove that any divisor on the chain of loops that is rational over the value group lifts to a divisor of the same rank on C, confirming a conjecture of Cools, Draisma, Robeva, and the third author.

AB - Let C be a curve over a complete valued field having an infinite residue field and whose skeleton is a chain of loops with generic edge lengths. We prove that any divisor on the chain of loops that is rational over the value group lifts to a divisor of the same rank on C, confirming a conjecture of Cools, Draisma, Robeva, and the third author.

KW - Brill-Noether theory

KW - Special divisors on algebraic curves

KW - Tropical geometry

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Lifting divisors on a generic chain of loops

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

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