On the Maximal Rank Conjecture for Line Bundles of Extremal Degree

TL;DR

This paper introduces a deformation theory-based method to prove the maximal rank conjecture for line bundles of extremal degree, providing new insights and confirming the conjecture in this specific case.

Contribution

The paper presents a novel deformation theory approach to establish the maximal rank conjecture for extremal degree line bundles, a key case for testing the conjecture.

Findings

Maximal rank conjecture holds for line bundles of extremal degree

New deformation theory method successfully applied to this case

Provides a proof for the conjecture in the extremal degree scenario

Abstract

We propose a new method, using deformation theory, to study the maximal rank conjecture. For line bundles of extremal degree, which can be viewed as the first case to test the conjecture, we prove that maximal rank conjecture holds by our new method.