Proof of Weierstrass gap theorem

TL;DR

This paper provides an expository proof of the Weierstrass gap theorem using cohomology terminology, analyzing gap sequences to identify gaps and non-gaps on algebraic curves.

Contribution

It offers a cohomology-based proof of the classical Weierstrass gap theorem, enhancing understanding through an alternative mathematical perspective.

Findings

Cohomology approach to the Weierstrass gap theorem

Identification of gap and non-gap sequences on algebraic curves

Clarification of the structure of gaps in algebraic geometry

Abstract

In this expository note we give proof of the Weierstrass gap theorem in Cohomology terminology. We analyze gap sequence for finding possible gaps and non-gaps on X.