Sheaf lines of Yang-Mills Instanton Sheaves

TL;DR

This paper investigates the geometric and singularity structures of sheaf lines in CP^3 related to SL(2,C) Yang-Mills instanton sheaves, revealing higher-order singularities and their implications for the instanton moduli space.

Contribution

It introduces the calculation of sheaf lines in CP^3 supporting instanton sheaves and analyzes their singularity structures, highlighting their unique higher-order singularities.

Findings

Sheaf lines are special jumping lines over S^4.

Singularity order at sheaf lines is higher than at normal jumping lines.

Conjecture that higher singularity order is a general feature of sheaf lines.

Abstract

We calculate a sheaf line in CP^3 which is the real line supporting sheaf points on CP^3 of SL(2,C) Yang-Mills instanton (or SU(2) complex Yang-Mills instanton) sheaves for some given ADHM data we obtained previously. We found that this sheaf line is indeed a special jumping line over S^4 spacetime. In addition, we calculate the singularity structure of the connection A and the field strength F at the corresponding singular point on S^4 of this sheaf line. We found that the order of singularity at the singular point on S^4 associated with the sheaf line in CP^3 is higher than those of other singular points associated with normal jumping lines. We conjecture that this is a general feature for sheaf lines among jumping lines.