On holonomic systems of microdifferential equations. III. Systems with regular singularities

On Holonomic Systems of Micro - differential Equations . Ill — Systems with Regular Singularities —

This is the third of the series of the papers dealing with holonomic systems(*. A holonomic system is, by definition, a left coherent (f-Module (or ^-Modules)* whose characteristic variety is Lagrangian. It shares the finiteness theorem with a linear ordinary differential equation, namely, all the cohomology groups associated with its solution sheaf are finite dimensional ([6], [12]). Hence the...

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...

Moduli of Regular Holonomic -modules with Normal Crossing Singularities

Hamilton equations for non-holonomic systems

Hamilton equations for Lagrangian systems on fibred manifolds, subjected to general non-holonomic constraints (i.e., not necessarily affine in the velocities) are studied. Conditions for existence of a non-holonomic Legendre transformation are discussed, and the corresponding formulas for constraint momenta and Hamiltonian are found.

On the Holonomic Systems of Linear Differential Equations , II *

In this paper we shall study the restriction of holonomic systems of differential equations. Let X be a complex manifold and Y a submanifold, and let (9 x and D x be the sheaf of the holomorphic functions and the sheaf of the differential operators of finite order, respectively. If a function u on X satisfies a system of differential equations, the restriction of u onto Y also satisfies the sys...