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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 morphismsfrom general Azumaya nodal curves, of genus $\ge 2$, with a fundamental moduleto 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 countermoduli stack to D-strings as the moduli stack of stable maps in Gromov-Wittentheory to the fundamental string. It serves and prepares for us the basistoward a new invariant of Calabi-Yau 3-fold that captures soft-D-stringworld-sheet instanton numbers in superstring theory. This note is writtenhand-in-hand with D(10.1) and is to be read side-by-side with ibidem.

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