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

References in corpus (1)

• Effective divisors on \bar{M}_g, curves on K3 surfaces and the Slope Conjecture

Cited by in corpus (17)

• Tropical Ideals
• The Maximal Rank Conjecture
• Realizability of tropical canonical divisors
• Hodge theory for tropical varieties
• The Kodaira dimensions of ${\overline{\mathcal{M}}}_{22}$ and ${\overline{\mathcal{M}}}_{23}$
• The strong maximal rank conjecture and moduli spaces of curves
• Prym-Brill-Noether Loci of special curves
• Limit linear series and ranks of multiplication maps
• Combinatorial and inductive methods for the tropical maximal rank conjecture
• On the strong maximal rank conjecture in genus 22 and 23
• The non-abelian Brill-Noether divisor on ${\overline{\mathcal{M}}}_{13}$ and the Kodaira dimension of ${\overline{\mathcal{R}}}_{13}$
• Quiver representations arising from degenerations of linear series, I
• Maximal Rank Divisors on ${\overline{\mathcal{M}}}_{g,n}$
• The automorphism group of $M_{0,n}^{\text{trop}}$ and ${\overline{M}}_{0,n}^{\text{trop}}$
• Scrollar Invariants of Tropical Curves
• Voronoi tilings, toric arrangements and degenerations of line bundles III
• Poincaré Series of Divisors on Graphs and Chains of Loops