Macaulay's theorem and local Torelli for weighted hypersurfaces
Matrices for Fenchel-Nielsen coordinates.
Modules des surfaces de Riemann
Moduli and classification of irregular Kaehler manifolds (and algebraic varieties) with Albanese general type fibrations.
Moduli for Kodaira surfaces
Moduli for pointed convex domains.
Moduli for Vectorbundles on Pn(C).
Moduli of half conformally flat structures.
Moduli of Open Holomorphic Maps of Compact Complex Manifolds.
Moduli of Parabolic G-bundles on Curves.
Moduli of Polarized Kahler Manifolds.
Moduli of pre-...-modules, preverse sheaves and the Riemann-Hilbert morphism. I.
Moduli of Vector Bundles on Curves with Parabolic Structures.
Moduli Spaces for Hopf Surfaces.
Moduli spaces of abelian differentials : the principal boundary, counting problems, and the Siegel-Veech constants
A holomorphic 1-form on a compact Riemann surface S naturally defines a flat metric on S with cone-type singularities. We present the following surprising phenomenon: having found a geodesic segment (saddle connection) joining a pair of conical points one can find with a nonzero probability another saddle connection on S having the same direction and the same length as the initial one. A similar phenomenon is valid for the families of parallel closed geodesics. We give a complete description of...
Moduli spaces of covers and the Hurwitz monodromy group.
Moduli spaces of holomorphic mappings into hyperbolically imbedded complex spaces and locally symmetric spaces.
Moduli spaces of Lie algebroid connections
We shall prove that the moduli space of irreducible Lie algebroid connections over a connected compact manifold has a natural structure of a locally Hausdorff Hilbert manifold. This generalizes some known results for the moduli space of simple semi-connections on a complex vector bundle over a compact complex manifold.
Moduli spaces of local systems and higher Teichmüller theory
Let G be a split semisimple algebraic group over Q with trivial center. Let S be a compact oriented surface, with or without boundary. We define positive representations of the fundamental group of S to G(R), construct explicitly all positive representations, and prove that they are faithful, discrete, and positive hyperbolic; the moduli space of positive representations is a topologically trivial open domain in the space of all representations. When S have holes, we defined two moduli spaces closely...
Moduli spaces of stable real algebraic curves