Vol. 8, No. 9, 2014

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ISSN: 1944-7833 (e-only)
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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
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