Espace de Teichmüller
Espaces de Moisezon relatifs et algébrisation des modifications analytiques.
Estimating the states of the Kauffman bracket skein module
The states of the title are a set of knot types which suffice to create a generating set for the Kauffman bracket skein module of a manifold. The minimum number of states is a topological invariant, but quite difficult to compute. In this paper we show that a set of states determines a generating set for the ring of characters of the fundamental group, which in turn provides estimates of the invariant.
Etude topologique des formes logarithmiques fermées.
Euler characteristics of moduli spaces of curves
Let be the moduli space of -pointed Riemann surfaces of genus . Denote by the Deligne-Mumford compactification of . In the present paper, we calculate the orbifold and the ordinary Euler characteristic of for any and such that .
Everywhere non reduced moduli spaces.
Existence and Degeneration of Kähler-Einstein Metrics on Minimal Algebraic Varieties of General Type.
Existence of sections of line bundles over a torodial group and its applications.
Exotic Deformations of Calabi-Yau Manifolds
We introduce Quantum Inner State manifolds (QIS manifolds) as (compact) -dimensional symplectic manifolds endowed with a -tamed almost complex structure and with a nowhere vanishing and normalized section of the bundle satisfying the condition .We study the moduli space of QIS deformations of a given Calabi-Yau manifold, computing its tangent space and showing that is non obstructed. Finally, we present several examples of QIS manifolds.
Exponential mixing for the Teichmüller flow
We study the dynamics of the Teichmüller flow in the moduli space of abelian differentials (and more generally, its restriction to any connected component of a stratum). We show that the (Masur-Veech) absolutely continuous invariant probability measure is exponentially mixing for the class of Hölder observables. A geometric consequence is that the action in the moduli space has a spectral gap.
Factorization of rank two theta functions. II. Proof of the Verlinde formula.
Familien komplexer Räume mit streng pseudokonvexer spezieller Faser
Families of varieties with prescribed singularities
Fibrés déterminants, déterminants régularisés et mesures sur les espaces de modules des courbes complexes
Fibrés stables et fibrés exceptionnels sur
Filtration de Harder-Narasimhan pour des fibrés complexes ou des faisceaux sans torsion
On généralise dans cet article la notion de filtration de Harder-Narasimhan au cas des fibrés complexes sur une variété presque complexe compacte d'une part, et au cas des faisceaux cohérents sans torsion sur une variété holomorphe d'autre part. On démontre, dans les deux cas, l'existence d'un déstabilisant maximal. On obtient un théorème de convergence en famille et par là-même l'ouverture de la stabilité en déformation.
Finite parts of the spectrum of a Riemann surface.
Finiteness results for Teichmüller curves
We show that for each genus there are only finitely many algebraically primitive Teichmüller curves , such that (i) lies in the hyperelliptic locus and (ii) is generated by an abelian differential with two zeros of order . We prove moreover that for these Teichmüller curves the trace field of the affine group is not only totally real but cyclotomic.
First Order Completeness Theorems.
Flag Structures on Seifert Manifolds.