Amenable coverings of complex manifolds and holomorphic probalitiy measures.
Amibes de variétés algébriques et dénombrement de courbes
Les amibesdes variétés algébriques dans sont les images de ces variétés par l’application des moments , . Des résultats obtenus par G. Mikhalkin montrent l’utilité des amibes pour l’étude des variétés algébriques réelles et complexes. Les amibes peuvent être déformées en des complexes polyédraux appelésvariétés algébriques tropicales. Cette déformation permet, en particulier, de calculer les invariants de Gromov-Witten du plan projectif et d’autres surfaces toriques en dénombrant des courbes...
An Algebraic Formula for the Index of a Vector Field on an Isolated Complete Intersection Singularity
Let be a germ of a complete intersection variety in , , having an isolated singularity at and be the germ of a holomorphic vector field having an isolated zero at and tangent to . We show that in this case the homological index and the GSV-index coincide. In the case when the zero of is also isolated in the ambient space we give a formula for the homological index in terms of local linear algebra.
An algorithm for finding the Veech group of an origami.
An analog of the Fefferman construction
The Fefferman construction associates to a manifold carrying a CR–structure a conformal structure on a sphere bundle over the manifold. There are some analogs to this construction, with one giving a Lie contact structure, a refinement of the contact bundle on the bundle of rays in the cotangent bundle of a manifold with a conformal metric. Since these structures are parabolic geometries, these constructions can be dealt with in this setting.
An analog of the Fubini-Studi form for two-dimensional toric varieties.
An analogue of convexity for complements of amoebas of varieties of higher codimension, an answer to a question asked by B. Sturmfels.
An analogue of holonomic -modules on smooth varieties in positive characteristics.
An analogy of Tian-Todorov theorem on deformations of CR-structures
An angle metric through the notion of Grassmann representative.
An application of a theorem of Huber in holomorphic foliation theory
An application of multivariate total positivity to peacocks
We use multivariate total positivity theory to exhibit new families of peacocks. As the authors of [F. Hirsch, C. Profeta, B. Roynette and M. Yor, Peacocks and associated martingales vol. 3. Bocconi-Springer (2011)], our guiding example is the result of Carr−Ewald−Xiao [P. Carr, C.-O. Ewald and Y. Xiao, Finance Res. Lett. 5 (2008) 162–171]. We shall introduce the notion of strong conditional monotonicity. This concept is strictly more restrictive than the conditional monotonicity as defined in [F....
An Approximate Riemann Mapping Theorem in Cn.
An approximation theorem related to good compact sets in the sense of Martineau
This note contains an approximation theorem that implies that every compact subset of is a good compact set in the sense of Martineau. The property in question is fundamental for the extension of analytic functionals. The approximation theorem depends on a finiteness result about certain polynomially convex hulls.
An arc-analytic function with nondiscrete singular set
We construct an arc-analytic function (i.e. analytic on every real-analytic arc) in ℝ² which is analytic outside a nondiscrete subset of ℝ².
An arithmetic characterisation of the symmetric monodromy groups of singularities.
An effective Matsusaka big theorem
An eigenvalue problem for the complex Monge-Ampère operator in pseudoconvex domains
An Elementary Approach to Hecke Operators.
An elementary proof of the Briançon-Skoda theorem
We give an elementary proof of the Briançon-Skoda theorem. The theorem gives a criterionfor when a function belongs to an ideal of the ring of germs of analytic functions at ; more precisely, the ideal membership is obtained if a function associated with and is locally square integrable. If can be generated by elements,it follows in particular that , where denotes the integral closure of an ideal .