Vol. 10, No. 8, 2016

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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

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.

Brill-Noether theory, tropical geometry, tropical independence, chain of loops, maximal rank conjecture, Gieseker-Petri
Mathematical Subject Classification 2010
Primary: 14H51
Secondary: 14T05
Received: 2 October 2015
Revised: 16 April 2016
Accepted: 31 May 2016
Published: 7 October 2016
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