Operations with regular holonomic D-modules with support a normal crossing

Moduli of regular holonomic D-modules with normal crossing singularities

This paper solves the global moduli problem for regular holonomic Dmodules with normal crossing singularities on a nonsingular complex projective variety. This is done by introducing a level structure (which gives rise to “pre-D-modules”), and then introducing a notion of (semi-)stability and applying Geometric Invariant Theory to construct a coarse moduli scheme for semistable pre-D-modules. A...

http://www.ictp.trieste.it/~pub_off IC/97/21 United Nations Educational Scientific and Cultural Organization and International Atomic Energy Agency INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS MODULI OF REGULAR HOLONOMIC D-MODULES WITH NORMAL CROSSING SINGULARITIES

This paper solves the global moduli problem for regular holonomic D-modules with normal crossing singularities on a nonsingular complex projective variety. This is done by introducing a level structure (which gives rise to "pre-D-modules"), and then introducing a notion of (semi-)stability and applying Geometric Invariant Theory to construct a coarse moduli scheme for semistable pre-D-modules. ...

Moduli of Regular Holonomic -modules with Normal Crossing Singularities

Microlocal study of ind-sheaves I: micro-support and regularity

We define the notions of micro-support and regularity for indsheaves, and prove their invariance by contact transformations. We apply the results to the ind-sheaves of temperate holomorphic solutions of D-modules. We prove that the micro-support of such an ind-sheaf is the characteristic variety of the corresponding D-module and that the ind-sheaf is regular if the D-module is regular holonomic.

Holonomic D-module with Betti structure

This is an attempt to define a notion of Betti structure with nice functorial property for algebraic holonomic D-modules which are not necessarily regular singular.