On Saito's normal crossing condition

Characterizing Normal Crossing Hypersurfaces

The objective of this article is to give an effective algebraic characterization of normal crossing hypersurfaces in complex manifolds. It is shown that a divisor (=hypersurface) has normal crossings if and only if it a free divisor, has a radical Jacobian ideal and a smooth normalization. Using K. Saito’s theory of free divisors, also a characterization in terms of logarithmic differential for...

The No-Upward-Crossing Condition and the Moral Hazard Problem

We revisit the first-order approach to the moral hazard problem. Our fundamental claim is that in well-behaved problems, a condition we term No Upward Crossing (NUC) holds. We show how NUC facilitates analysis by both simplifying the relevant conditions for the validity of the first-order approach and giving them an economic interpretation. We provide extensive analysis of sufficient conditions...

Hörmander’s Condition for Normal Bundles on Spaces of Immersions

Several representations of geometric shapes involve quotients of mapping spaces. The projection onto the quotient space defines two subbundles of the tangent bundle, called the horizontal and vertical bundle. We investigate in these notes the sub-Riemannian geometries of these bundles. In particular, we show for a selection of bundles which naturally occur in applications that they are either b...

A Hall Condition for Normal Hypergraphs

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...