A note on the Lawrence-Krammer-Bigelow representation.
A note on the Nullstellensatz for c-holomorphic functions
We begin this article with a graph theorem and a kind of Nullstellensatz for weakly holomorphic functions. This yields a general Nullstellensatz for c-holomorphic functions on locally irreducible sets. In Section 2 some methods of Płoski-Tworzewski permit us to prove an effective Nullstellensatz for c-holomorphic functions in the case of a proper intersection with the degree of the intersection cycle as exponent. We also extend this result to the case of isolated improper intersection, generalizing...
A note on the regularity of the degenerate complex Monge-Ampère equation
We prove the almost regularity of the degenerate complex Monge-Ampère equation in a special case.
A notion of boundedness for hyperfunctions and Massera type theorems
For some classes of periodic linear ordinary differential equations and functional equations, it is known that the existence of a bounded solution in the future implies the existence of a periodic solution. In order to think on such phenomena for hyperfunction solutions to linear functional equations, we introduced a notion of bounded hyperfunctions, and translated the problems into the problems on analytic solutions to some equations in complex domains. In this article, after...
A notion of extremal analytic discs related to interpolation in the ball.
A p-adic Nevanlinna-Diophantine correspondence
A Peak Set of Hausdorff Dimension 2n? 1 for the Algebra A(D) in the Boundary of a Domain D with C°°-Boundary in Cn.
A pointwise growth estimate for analytic functions in tubes.
A precise result on the boundary regularity of biholomorphic mappings (Erratum).
A Precise Result on the Boundary Regularity of Biholomorphic Mappings.
A Priori Estimates and a Liouvielle Theorem for Complex Monge-Ampère Equations.
A priori estimates for weak solutions of complex Monge-Ampère equations
Let be a compact Kähler manifold and be a smooth closed form of bidegree which is nonnegative and big. We study the classes of -plurisubharmonic functions of finite weighted Monge-Ampère energy. When the weight has fast growth at infinity, the corresponding functions are close to be bounded. We show that if a positive Radon measure is suitably dominated by the Monge-Ampère capacity, then it belongs to the range of the Monge-Ampère operator on some class . This is done by establishing...
A product formula for period integrals.
A proof of the birationality of certain BHK-mirrors
We generalize and give an elementary proof of Kelly’s refinement [9] of Shoemaker’s result [11] on the birationality of certain BHK-mirrors. Our approach uses a construction that is equivalent to the Krawitz generalization [10] of the duality in Berglund-Hübsch [2].
A proof of the stratified Morse inequalities for singular complex algebraic curves using the Witten deformation
The Witten deformation is an analytic method proposed by Witten which, given a Morse function on a smooth compact manifold , allows to prove the Morse inequalities. The aim of this article is to generalise the Witten deformation to stratified Morse functions (in the sense of stratified Morse theory as developed by Goresky and MacPherson) on a singular complex algebraic curve. In a previous article the author developed the Witten deformation for the model of an algebraic curve with cone-like singularities...
A proof of the valuation property and preparation theorem
The purpose of this article is to present a short model-theoretic proof of the valuation property for a polynomially bounded o-minimal theory T. The valuation property was conjectured by van den Dries, and proved for the polynomially bounded case by van den Dries-Speissegger and for the power bounded case by Tyne. Our proof uses the transfer principle for the theory (i.e. T with an extra unary symbol denoting a proper convex subring), which-together with quantifier elimination-is due to van den...
A property of determining sets for analytic functions
À propos de G. A. G. R.
À propos de la forme hermitienne canonique d'une singularité isolée d'hypersurface
A propos de revêtements ramifiés d'espaces de Stein.