The Maximal Rank Conjecture

TL;DR

This paper proves the Maximal Rank Conjecture, establishing the Hilbert function for general curves embedded in projective space, which advances understanding of algebraic geometry and curve embeddings.

Contribution

It provides a proof of the Maximal Rank Conjecture for general curves, resolving a longstanding open problem in algebraic geometry.

Findings

Confirmed the Maximal Rank Conjecture for general curves

Determined the Hilbert function of embedded general curves

Resolved a major open problem in algebraic geometry

Abstract

Let C be a general curve of genus g, embedded in P^r via a general linear series of degree d. In this paper, we prove the Maximal Rank Conjecture, which determines the Hilbert function of C.