Moduli of regular holonomic $\mathcal{D}_X$-modules with natural parabolic stability

Abstract

In this paper we re-visit the moduli problem for regular holonomic $\mathcal{D}$-modules with normal crossing singularities, and give a new definition of semistability, more general than the older notion, construct the moduli scheme, and describe its points. Independently of this, we introduce another natural parabolic notion of stability for such $\mathcal{D}$-modules, and construct the moduli in a special case.