Algebra & Number Theory
- Algebra Number Theory
- Volume 10, Number 8 (2016), 1601-1640.
Tropical independence, II: The maximal rank conjecture for quadrics
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.
Algebra Number Theory, Volume 10, Number 8 (2016), 1601-1640.
Received: 2 October 2015
Revised: 16 April 2016
Accepted: 31 May 2016
First available in Project Euclid: 16 November 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14H51: Special divisors (gonality, Brill-Noether theory)
Secondary: 14T05: Tropical geometry [See also 12K10, 14M25, 14N10, 52B20]
Jensen, David; Payne, Sam. Tropical independence, II: The maximal rank conjecture for quadrics. Algebra Number Theory 10 (2016), no. 8, 1601--1640. doi:10.2140/ant.2016.10.1601. https://projecteuclid.org/euclid.ant/1510842582