Cohomology with -bounds on polycylinders.
Coleff-Herrera currents, duality, and noetherian operators
Let be a coherent subsheaf of a locally free sheaf and suppose that has pure codimension. Starting with a residue current obtained from a locally free resolution of we construct a vector-valued Coleff-Herrera current with support on the variety associated to such that is in if and only if . Such a current can also be derived algebraically from a fundamental theorem of Roos about the bidualizing functor, and the relation between these two approaches is discussed. By a construction...
Colmatage de surfaces holomorphes et classification des surfaces compactes
On considère le problème du colmatage en dimension 2, où l’on examine sous quelle condition une hypersurface strictement pseudoconvexe dans une surface holomorphe est le bord d’un espace de Stein. On montre que l’exemple de Rossi d’une hypersurface strictement pseudoconvexe , qui est le bord de deux domaines non relativement compacts, n’est jamais le bord d’un espace de Stein bien que les fonctions holomorphes définies dans un voisinage de donnent des cartes locales. On démontre que dans une...
Combinations of rational singularities on plane sextic curves with the sum of Milnor numbers less than sixteen
Common Fixed Points of Commuting Holomorphic Maps.
Commutant of multiplication operators in weighted Bergman spaces on polydisk
We study a certain operator of multiplication by monomials in the weighted Bergman space both in the unit disk of the complex plane and in the polydisk of the -dimensional complex plane. Characterization of the commutant of such operators is given.
Commutation properties and Lipschitz estimates for the Bergman and Szegö projections.
Commuting holomorphic maps in strongly convex domains
Compact complex manifolds with numerically effective cotangent bundles.
Compact complex threefolds of class L associated to polynomial automorphisms of C3.
We construct new families of non-Kähler compact complex threefolds belonging to Kato's Class L. The construction uses certain polynomial automorphisms of C3. We also study basic properties of our manifolds.
Compact Differentiable 4-Folds with Quaternionic Structures.
Compact Differentiable 4-Folds with Quaternionic Structures (Erratum).
Compact Kähler manifolds with compactifiable universal cover
In this appendix, we observe that Iitaka’s conjecture fits in the more general context of special manifolds, in which the relevant statements follow from the particular cases of projective and simple manifolds.
Compact Kähler manifolds with hermitian semipositive anticanonical bundle
Compact Kähler manifolds with nonnegatively curvature operator.
Compact lcK manifolds with parallel vector fields
We show that for n > 2 a compact locally conformally Kähler manifold (M2n , g, J) carrying a nontrivial parallel vector field is either Vaisman, or globally conformally Kähler, determined in an explicit way by a compact Kähler manifold of dimension 2n − 2 and a real function.
Compact manifold of coherent states invariant by semisimple Lie groups
Compact moduli spaces of stable sheaves over non-algebraic surfaces.
Compact quotients of large domains in complex projective space
We study compact complex manifolds covered by a domain in -dimensional projective space whose complement is non-empty with -dimensional Hausdorff measure zero. Such manifolds only exist for . They do not belong to the class , so they are neither Kähler nor Moishezon, their Kodaira dimension is , their fundamental groups are generalized Kleinian groups, and they are rationally chain connected. We also consider the two main classes of known 3-dimensional examples: Blanchard manifolds, for which...
Compact subsets of preserving Markov’s inequality