Primitive Holomorphic Maps of Curves.
Projectivity of Kähler manifolds – Kodaira’s problem
Every compact Kähler surface is deformation equivalent to a projective surface. In particular, topologically Kähler surfaces and projective surfaces cannot be distinguished. Kodaira had asked whether this continues to hold in higher dimensions. We explain the construction of a series of counter-examples due to C. Voisin, which yields compact Kähler manifolds of dimension at least four whose rational homotopy type is not realized by any projective manifold.
Properties of an abstract pseudoresolvent and well-posedness of the degenerate Cauchy problem
The degenerate Cauchy problem in a Banach space is studied on the basis of properties of an abstract analytical function, satisfying the Hilbert identity, and a related pair of operators A, B.
Proprietà di trasversalità per il tensore di Nijenhuis di una varietà quasi complessa
Propriétés de ramification à l'infini du groupe modulaire de Teichmüller. With an appendix in English by Ken Baclawski
Quantum Cohomology and Periods
In a previous paper, the author introduced an integral structure in quantum cohomology defined by the -theory and the Gamma class and showed that it is compatible with mirror symmetry for toric orbifolds. Applying the quantum Lefschetz principle to the previous results, we find an explicit relationship between solutions to the quantum differential equation of toric complete intersections and the periods (or oscillatory integrals) of their mirrors. We describe in detail the mirror isomorphism of...
Quasiconformal homeomorphisms on CR 3-manifolds with symmetries.
Quasiconformality of pseudo-conformal transformations and deformations of hypersurfaces in C...
Real algebraic curves in the moduli space of complex curves
Real projective structures on Riemann surfaces
Real Structure of Teichmüller spaces.
Rectifiability in Teichmüller theory
Regularity and extremality of quasiconformal homeomorphisms on CR 3-manifolds.
Relations between holomorphic quadratic differentials II
Relations monomiales entre périodes p-adiques.
Représentations linéaires des groupes kählériens et de leurs analogues projectifs
Dans cette note nous établissons le résultat suivant, annoncé dans [CCE13] : si est l’image d’une représentation linéaire d’un groupe kählérien , il admet un sous-groupe d’indice fini qui est l’image d’une représentation linéaire du groupe fondamental d’une variété projective complexe lisse .Il s’agit donc de la solution (à indice fini près) pour les représentations linéaires d’une question usuelle demandant si le groupe fondamental d’une variété kählérienne compacte est aussi celui d’une variété...
Resultados de F. Cano sobre una conjetura de Thom.
Réversibilité et classification des centres nilpotents
Nous considérons un germe de 1-forme analytique dans dont le 1-jet est . Nous montrons que si l’équation définit un centre (i.e toutes les courbes solutions sont des cycles) il existe une involution analytique de préservant le portrait de phase du système. Géométriquement ceci signifie que les centres analytiques nilpotents sont obtenus par image réciproque par des applications pli. Un théorème de conjugaison équivariante permet d’obtenir une classification complète de ces centres.
Riemann surfaces with boundary and natural triangulations of the Teichmüller space
We compare some natural triangulations of the Teichmüller space of hyperbolic surfaces with geodesic boundary and of some bordifications. We adapt Scannell–Wolf’s proof to show that grafting semi-infinite cylinders at the ends of hyperbolic surfaces with fixed boundary lengths is a homeomorphism. This way, we construct a family of equivariant triangulations of the Teichmüller space of punctured surfaces that interpolates between Bowditch–Epstein–Penner’s (using the spine construction) and Harer–Mumford–Thurston’s...
Rigidity for variations of Hodge structure and Arakelov-type finiteness theorems