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
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