Two Ext groups and a residue

TL;DR

This paper presents a key lemma crucial for advancing the proof of the Green-Griffiths conjecture for certain algebraic surfaces, filling a significant gap in the existing mathematical framework.

Contribution

It introduces a new lemma involving Ext groups and residues that completes a missing step in the author's proof of the Green-Griffiths conjecture for specific surfaces.

Findings

Key lemma established for surfaces with enough 2-jets

Advances proof of Green-Griffiths conjecture in particular cases

Provides a guide to the overall proof structure

Abstract

The present constitutes the key lemma which was hitherto missing in the author's proof of, inter alia, the Green-Griffiths conjecture for surfaces with enough 2-jets, e.g. $13\mathrm{c}_1^2> 9\mathrm{c}_2$. As to why this is so is not the immediate concern of this article since it is a lemma within a whole. By way of what is essentially an appendix to the current paper, a guide to the whole is provided at http://www.mat.uniroma2.it/~mcquilla.