Tropical independence II: The maximal rank conjecture for quadrics

Abstract

Building on our earlier results on tropical independence and shapes of divisors in tropical linear series, we give a tropical proof of the maximal rank conjecture for quadrics. We also prove a tropical analogue of Max Noether's theorem on quadrics containing a canonically embedded curve, and state a combinatorial conjecture about tropical independence on chains of loops that implies the maximal rank conjecture for algebraic curves.

30 pages, 13 figures. v2: Removed characteristic zero hypothesis from Theorem 1.2, minor expository improvements