Vol. 2, No. 6, 2008

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Specialization of linear systems from curves to graphs

Matthew Baker

Appendix: Brian Conrad

Vol. 2 (2008), No. 6, 613–653
Abstract

We investigate the interplay between linear systems on curves and graphs in the context of specialization of divisors on an arithmetic surface. We also provide some applications of our results to graph theory, arithmetic geometry, and tropical geometry.

Keywords
arithmetic surface, specialization, dual graph, reduction graph, Brill–Noether theory, Weierstrass point, tropical geometry
Mathematical Subject Classification 2000
Primary: 14H25, 05C99
Secondary: 14H51, 14H55
Milestones
Received: 21 February 2008
Revised: 13 May 2008
Accepted: 12 June 2008
Published: 14 October 2008
Authors
Matthew Baker
School of Mathematics
Georgia Institute of Technology
Atlanta, GA 30332-0160
United States
Brian Conrad