Vol. 8, No. 9, 2014

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

Volume 15, 1 issue

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
Editorial Board
Editors’ Interests
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
Other MSP Journals
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

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.

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
Received: 24 January 2014
Revised: 7 September 2014
Accepted: 19 October 2014
Published: 28 December 2014
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