Permanence of local properties under hyperplane sections
Picard-Zahlen komplexer Tori.
Pluricanonical embeddings
Pluriclosed flow on manifolds with globally generated bundles
We show global existence and convergence results for the pluriclosed flow on manifolds for which certain naturally associated tensor bundles are globally generated.
Polarized Mixed Hodge Structures and the Local Monodromy of a Variation of Hodge Structure.
Products of harmonic forms and rational curves.
Projective varieties invariant by one-dimensional foliations.
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.
Projektive Einbettung komplexer Mannigfaltigkeiten.
Proof of Nadel’s conjecture and direct image for relative -theory
A “relative” -theory group for holomorphic or algebraic vector bundles on a compact or quasiprojective complex manifold is constructed, and Chern-Simons type characteristic classes are defined on this group in the spirit of Nadel. In the projective case, their coincidence with the Abel-Jacobi image of the Chern classes of the bundles is proved. Some applications to families of holomorphic bundles are given and two Riemann-Roch type theorems are proved for these classes.
Pull-back of currents by meromorphic maps
Let and be compact Kähler manifolds, and let be a dominant meromorphic map. Based upon a regularization theorem of Dinh and Sibony for DSH currents, we define a pullback operator for currents of bidegrees of finite order on (and thus foranycurrent, since is compact). This operator has good properties as may be expected. Our definition and results are compatible to those of various previous works of Meo, Russakovskii and Shiffman, Alessandrini and Bassanelli, Dinh and Sibony, and can...
Pulling back cohomology classes and dynamical degrees of monomial maps
We study the pullback maps on cohomology groups for equivariant rational maps (i.e., monomial maps) on toric varieties. Our method is based on the intersection theory on toric varieties. We use the method to determine the dynamical degrees of monomial maps and compute the degrees of the Cremona involution.
Quadratic forms and singularities of genus one or two
We study singularities obtained by the contraction of the maximal divisor in compact (non-kählerian) surfaces which contain global spherical shells. These singularities are of genus 1 or 2, may be -Gorenstein, numerically Gorenstein or Gorenstein. A family of polynomials depending on the configuration of the curves computes the discriminants of the quadratic forms of these singularities. We introduce a multiplicative branch topological invariant which determines the twisting coefficient of a non-vanishing...
Quelques propriétés arithmétiques des surfaces rationnelles (d'après Manin)
Réduction algébrique d'un morphisme faiblement Kählérien propre et applications.
Réduction d'albanèse d'un morphisme propre et faiblement kahlérien. II. Groupes d'automorphismes relatifs
Réduction d'albanèse d'un morphisme propre et faiblement kahlérien. I
Relevements modulo p2 et decomposition du complexe de de Rham.
Remarques sur le revêtement universel des variétés kählériennes compactes
Réseaux de Kummer et surfaces K3.