A mathematical theory of D-string world-sheet instantons, II: Moduli stack of $Z$-(semi)stable morphisms from Azumaya nodal curves with a fundamental module to a projective Calabi-Yau 3-fold

TL;DR

This paper develops a moduli stack of Z-semistable morphisms from Azumaya nodal curves to Calabi-Yau 3-folds, providing a foundation for new string theory invariants related to D-string instantons.

Contribution

It introduces the notion of Z-semistable morphisms from Azumaya curves, proving the compactness of their moduli stack, and sets the stage for defining new Calabi-Yau invariants.

Findings

Moduli stack of Z-semistable morphisms is compact.

Defines a counter moduli stack to D-strings as stable maps.

Lays groundwork for new superstring invariants.

Abstract

In this Part II, D(10.2), of D(10), we take D(10.1) (arXiv:1302.2054 [math.AG]) as the foundation to define the notion of $Z$-semistable morphisms from general Azumaya nodal curves, of genus $\ge 2$, with a fundamental module to a projective Calabi-Yau 3-fold and show that the moduli stack of such $Z$-semistable morphisms of a fixed type is compact. This gives us a counter moduli stack to D-strings as the moduli stack of stable maps in Gromov-Witten theory to the fundamental string. It serves and prepares for us the basis toward a new invariant of Calabi-Yau 3-fold that captures soft-D-string world-sheet instanton numbers in superstring theory. This note is written hand-in-hand with D(10.1) and is to be read side-by-side with ibidem.