
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 . Our main technique is the Bogomolov-Gieseker type inequality for proved by Macri.
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