Tropical independence II: The maximal rank conjecture for quadrics

TL;DR

This paper provides a tropical geometric proof of the maximal rank conjecture for quadrics, extending previous work on tropical independence and establishing new combinatorial conjectures related to algebraic curves.

Contribution

It offers a tropical proof of the maximal rank conjecture for quadrics and introduces a combinatorial conjecture linking tropical independence to algebraic curve properties.

Findings

Tropical proof of the maximal rank conjecture for quadrics

A tropical analogue of Max Noether's theorem

A new combinatorial conjecture on tropical independence

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.