Tropical independence I: Shapes of divisors and a proof of the Gieseker–Petri theorem

Jensen, David; Payne, Sam

doi:10.2140/ant.2014.8.2043

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Tropical independence I: Shapes of divisors and a proof of the Gieseker–Petri theorem

David Jensen and Sam Payne

Vol. 8 (2014), No. 9, 2043–2066

DOI: 10.2140/ant.2014.8.2043

Abstract

We develop a framework to apply tropical and nonarchimedean analytic methods to multiplication maps for linear series on algebraic curves, studying degenerations of these multiplications maps when the special fiber is not of compact type. As an application, we give a new proof of the Gieseker–Petri theorem, including an explicit tropical criterion for a curve over a valued field to be Gieseker–Petri general.

Keywords

tropical Brill–Noether theory, tropical independence, nonarchimedean geometry, Gieseker–Petri theorem, chain of loops, multiplication maps, Poincaré–Lelong

Mathematical Subject Classification 2010

Primary: 14T05

Secondary: 14H51

Milestones

Received: 24 January 2014

Revised: 7 September 2014

Accepted: 19 October 2014

Published: 28 December 2014

Authors

David Jensen
Department of Mathematics University of Kentucky 719 Patterson Office Tower Lexington, KY 40506 United States

Sam Payne
Department of Mathematics Yale University 10 Hillhouse Avenue New Haven, CT 06511 United States

Vol. 8, No. 9, 2014