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

Primary: 14H25, 05C99

Secondary: 14H51, 14H55

Authors

Appendix Authors