Arithmetic genus of integral space curves

TL;DR

This paper estimates the arithmetic genus of integral space curves not contained in certain surfaces, utilizing a Bogomolov-Gieseker type inequality on projective three-space to derive bounds.

Contribution

It introduces a new estimation method for the arithmetic genus of space curves using advanced stability inequalities.

Findings

Provides bounds for the arithmetic genus of integral space curves

Utilizes Bogomolov-Gieseker inequality in a novel context

Enhances understanding of space curve geometry

Abstract

We give an estimation for the arithmetic genus of an integral space curve, which are not contained in a surface of degree $k-1$. Our main technique is the Bogomolov-Gieseker type inequality for $\mathbb{P}^3$ proved by Macri.