Tropical independence II: The maximal rank conjecture for quadrics

David Jensen, Sam Payne

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

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.

Original languageEnglish
Pages (from-to)1601-1640
Number of pages40
JournalAlgebra and Number Theory
Volume10
Issue number8
DOIs
StatePublished - 2016

Bibliographical note

Publisher Copyright:
© 2016 Mathematical Sciences Publishers.

Keywords

  • Brill-noether theory
  • Chain of loops
  • Gieseker-petri
  • Maximal rank conjecture
  • Tropical geometry
  • Tropical independence

ASJC Scopus subject areas

  • Algebra and Number Theory

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