Towards the Bertram-Feinberg-Mukai Conjecture

TL;DR

This paper proves new cases of the Bertram-Feinberg-Mukai Conjecture using degeneration techniques, advancing understanding of rank two limit linear series and contributing tools for higher-rank Brill-Noether problems.

Contribution

It establishes the existence of solutions for an infinite family of cases of the conjecture, improving previous results and developing new analytical tools.

Findings

Proved the conjecture for new infinite family cases

Enhanced methods for analyzing moduli of limit linear series

Provided tools applicable to higher-rank Brill-Noether problems

Abstract

In this paper, we prove the existence portion of the Bertram-Feinberg-Mukai Conjecture for an infinite family of new cases using degeneration technique. This not only leads to a substantial improvement of known results but also develops finer tools for analyzing the moduli of rank two limit linear series which should be useful for other applications to other higher-rank Brill-Noether Problems.