On Decomposition Theorems for Hardy Spaces on Domains in ... and Applications.
On Deligne-Malgrange lattices, resolution of turning points and harmonic bundles
In this short survey, we would like to overview the recent development of the study on Deligne-Malgrange lattices and resolution of turning points for algebraic meromorphic flat bundles. We also explain their relation with wild harmonic bundles. The author hopes that it would be helpful for access to his work on wild harmonic bundles.
On direct and inverse images of D-Modules in prime characteristic.
On Dolbeault Cohomology and Envelopes of Holomorphy.
On Equivalence of Ideals of Real Global Analytic Functions and the 17th Hilbert Problem.
On Essential Singularities of Meromorphic Mappings.
On extensions of holomorphic functions satisfying a polynomial growth condition on algebraic varieties in
Let be an algebraic variety in and when is an integer then denotes all holomorphic functions on satisfying for all and some constant . We estimate the least integer such that every admits an extension from into by a polynomial , of degree at most. In particular is related to cohomology groups with coefficients in coherent analytic sheaves on . The existence of the finite integer is for example an easy consequence of Kodaira’s Vanishing Theorem.
On global Nash functions
On Hilbert's 17th Problem and Real Nullstellensatz for Global Analytic Functions.
On improper isolated intersection in complex analytic geometry
On irreducible components of a Weierstrass-type variety
We give a characterization of the irreducible components of a Weierstrass-type (W-type) analytic (resp. algebraic, Nash) variety in terms of the orbits of a Galois group associated in a natural way to this variety. Since every irreducible variety of pure dimension is (locally) a component of a W-type variety, this description may be applied to any such variety.
On Kodaira energy and adjoint reduction of polarized manifold.
On k-Pseudoflat Complex Spaces.
On local images of holomorphic mappings
On meromorphic functions defined by a differential system of order
Given a germ of holomorphic function on , we study the condition: “the ideal is generated by operators of order1”. We obtain here full characterizations in the particular cases of Koszul-free germs and unreduced germs of plane curves. Moreover, we prove that this condition holds for a special type of hyperplane arrangements. These results allow us to link this condition to the comparison of de Rham complexes associated with .
On microlocal -function
On Noether and strict stability, Hilbert exponent, and relative Nullstellensatz
Conditions characterizing the membership of the ideal of a subvariety arising from (effective) divisors in a product complex space Y × X are given. For the algebra of relative regular functions on an algebraic variety V, the strict stability is proved, in the case where Y is a normal space, and the Noether stability is established under a weakened condition. As a consequence (for both general and complete intersections) a global Nullstellensatz is derived for divisors in , respectively, . Also...
On non-holonomic irreducible D-modules.
On normalization of Nash varieties
On proper discs in complex manifolds
Let be a complex manifold of dimension at least which has an exhaustion function whose Levi form has at each point at least strictly positive eigenvalues. We construct proper holomorphic discs in through any given point and in any given direction.