Algebra & Number Theory

Tropical independence, II: The maximal rank conjecture for quadrics

David Jensen and Sam Payne

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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.

Article information

Source
Algebra Number Theory, Volume 10, Number 8 (2016), 1601-1640.

Dates
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
https://projecteuclid.org/euclid.ant/1510842582

Digital Object Identifier
doi:10.2140/ant.2016.10.1601

Mathematical Reviews number (MathSciNet)
MR3556794

Zentralblatt MATH identifier
1379.14020

Subjects
Primary: 14H51: Special divisors (gonality, Brill-Noether theory)
Secondary: 14T05: Tropical geometry [See also 12K10, 14M25, 14N10, 52B20]

Keywords
Brill-Noether theory tropical geometry tropical independence chain of loops maximal rank conjecture Gieseker-Petri

Citation

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


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