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 language | English |
|---|---|
| Pages (from-to) | 1601-1640 |
| Number of pages | 40 |
| Journal | Algebra and Number Theory |
| Volume | 10 |
| Issue number | 8 |
| DOIs | |
| State | Published - 2016 |
Bibliographical note
Funding Information:We thank D. Abramovich, E. Ballico, G. Farkas, C. Fontanari, E. Larson, and D. Ranganathan for helpful conversations related to this work and comments on earlier versions of this paper. Payne was supported in part by NSF CAREER DMS-1149054 and is grateful for ideal working conditions at the Institute for Advanced Study in spring 2015.
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