Modulräume holomorpher Abbildungen auf konkaven komplexen Räumen
Modulräume stabiler 2-Bündel auf Regelflächen.
Modultheorie hyperelliptischer Mumfordkurven.
Modulus of analytic classification for the generic unfolding of a codimension 1 resonant diffeomorphism or resonant saddle
We consider germs of one-parameter generic families of resonant analytic diffeomorphims and we give a complete modulus of analytic classification by means of the unfolding of the Écalle modulus. We describe the parametric resurgence phenomenon. We apply this to give a complete modulus of orbital analytic classification for the unfolding of a generic resonant saddle of a 2-dimensional vector field by means of the unfolding of its holonomy map. Here again the modulus is an unfolding of the Martinet-Ramis...
Moebius-invariant algebras in balls
It is proved that the Fréchet algebra has exactly three closed subalgebras which contain nonconstant functions and which are invariant, in the sense that whenever and is a biholomorphic map of the open unit ball of onto . One of these consists of the holomorphic functions in , the second consists of those whose complex conjugates are holomorphic, and the third is .
Moisezon Spaces and Almost Positive Coherent Sheaves.
Monge-Ampère boundary measures
We study swept-out Monge-Ampère measures of plurisubharmonic functions and boundary values related to those measures.
Monge-Ampère Equations, Geodesics and Geometric Invariant Theory
Existence and uniqueness theorems for weak solutions of a complex Monge-Ampère equation are established, extending the Bedford-Taylor pluripotential theory. As a consequence, using the Tian-Yau-Zelditch theorem, it is shown that geodesics in the space of Kähler potentials can be approximated by geodesics in the spaces of Bergman metrics. Motivation from Donaldson’s program on constant scalar curvature metrics and Yau’s strategy of approximating Kähler metrics by Bergman metrics is also discussed....
Monge-Ampère measures and Poletsky-Stessin Hardy spaces on bounded hyperconvex domains
Poletsky-Stessin Hardy (PS-Hardy) spaces are the natural generalizations of classical Hardy spaces of the unit disc to general bounded, hyperconvex domains. On a bounded hyperconvex domain Ω, the PS-Hardy space is generated by a continuous, negative, plurisubharmonic exhaustion function u of the domain. Poletsky and Stessin considered the general properties of these spaces and mainly concentrated on the spaces where the Monge-Ampère measure has compact support for the associated exhaustion...
Monodromie et pôles du prolongement méromorphe de
Monodromy and topological classification of germs of holomorphic foliations
We give a complete topological classification of germs of holomorphic foliations in the plane under rather generic conditions. The key point is the introduction of a new topological invariant called monodromy representation. This monodromy contains all the relevant dynamical information, in particular the projective holonomy representations whose topological invariance was conjectured in the eighties by Cerveau and Sad and is proved here under mild hypotheses.
Monodromy and weight filtration for smoothings of isolated singularities
Monodromy conjecture for some surface singularities
Monodromy groups of the projective structures on punctured surfaces.
Monodromy of a class of logarithmic connections on an elliptic curve.
Monodromy of a family of hypersurfaces
Let be an -dimensional irreducible smooth complex projective variety embedded in a projective space. Let be a closed subscheme of , and be a positive integer such that is generated by global sections. Fix an integer , and assume the general divisor is smooth. Denote by the quotient of by the cohomology of and also by the cycle classes of the irreducible components of dimension of . In the present paper we prove that the monodromy representation on for the family of smooth...
Monodromy of a family of hypersurfaces containing a given subvariety
Monodromy of functions defined on isolated singularities of complete intersections
Monodromy of hypergeometric functions and non-lattice integral monodromy
Monodromy zeta-functions of deformations and Newton diagrams.