Tropical independence, II: The maximal rank conjecture for quadrics

Jensen, David; Payne, Sam

doi:10.2140/ant.2016.10.1601

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Tropical independence, II: The maximal rank conjecture for quadrics

David Jensen and Sam Payne

Vol. 10 (2016), No. 8, 1601–1640

DOI: 10.2140/ant.2016.10.1601

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.

Keywords

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

Mathematical Subject Classification 2010

Primary: 14H51

Secondary: 14T05

Milestones

Received: 2 October 2015

Revised: 16 April 2016

Accepted: 31 May 2016

Published: 7 October 2016

Authors

David Jensen
Department of Mathematics 719 Patterson Office Tower Lexington, KY 40506-0027 United States

Sam Payne
Mathematics Department Yale University 10 Hillhouse Ave New Haven, CT 06511 United States

Vol. 10, No. 8, 2016