A geometrical approach to the theory of Jacobi forms
A vanishing theorem for Dolbeault cohomology of homogeneous vector bundles.
A vanishing theorem on arithmetic surfaces.
An effective version of Nor's theorem.
Asymptotic cohomology vanishing and a converse to the Andreotti-Grauert theorem on surfaces
In this paper, we study relations between positivity of the curvature and the asymptotic behavior of the higher cohomology group for tensor powers of a holomorphic line bundle. The Andreotti-Grauert vanishing theorem asserts that partial positivity of the curvature implies asymptotic vanishing of certain higher cohomology groups. We investigate the converse implication of this theorem under various situations. For example, we consider the case where a line bundle is semi-ample or big. Moreover,...
Asymptotic invariants of base loci
The purpose of this paper is to define and study systematically some asymptotic invariants associated to base loci of line bundles on smooth projective varieties. The functional behavior of these invariants is related to the set-theoretic behavior of base loci.
Automorphisms and local rigidity of regular varieties
Bornes pour la régularité de Castelnuovo-Mumford des schémas non lisses
Nous montrons dans cet article des bornes pour la régularité de Castelnuovo-Mumford d’un schéma admettant des singularités, en fonction des degrés des équations définissant le schéma, de sa dimension et de la dimension de son lieu singulier. Dans le cas où les singularités sont isolées, nous améliorons la borne fournie par Chardin et Ulrich et dans le cas général, nous établissons une borne doublement exponentielle en la dimension du lieu singulier.
Cohomologie des fibrés en droites sur les variétés magnifiques de rang minimal
Le théorème de Borel-Weil-Bott décrit la cohomologie des fibrés en droites sur les variétés de drapeaux. On généralise ici ce théorème à une plus grande classe de variétés projectives : les variétés magnifiques de rang minimal.
Concerning the existence of nice components in the Hilbert scheme of curves in ...n for n = 4 and 5.
Effective freeness of adjoint line bundles.
Effective nonvanishing, effective global generation
We prove a multiple-points higher-jets nonvanishing theorem by the use of local Seshadri constants. Applications are given to effectivity problems such as constructing rational and birational maps into Grassmannians, and the global generation of vector bundles.
Endlichkeits- und Verschwindungssätze für (schwach-) konstruierbare Garbenkomplexe auf komplexen Räumen.
Generalized Koszul complexes and Hochschild (co-)homology of complete intersections.
Geometric genera for ample vector bundles with regular sections.
Let X be a smooth complex projective variety of dimension n ≥ 3. A notion of geometric genus pg(X,E) for ample vector bundles E of rank r < n on X admitting some regular sections is introduced. The following inequality holds: pg(X,E) ≥ hn-r,0(X). The question of characterizing equality is discussed and the answer is given for E decomposable of corank 2. Some conjectures suggested by the result are formulated.
Hodge type of subvarieties of compact hermitian symmetric spaces.
Hodge type of subvarieties of IPn of small degrees.
Kodaira vanishing theorems on non-complete algebraic manifolds.
Koszul cohomology and -normality of a projective variety.
Moduli of certain Fano 4-folds.
In this brief note we give a proof that a certain family of Fano 4-folds, described below, is complex (locally) complete and effectively parametrized in the sense of Kodaira-Spencer [Ko-Sp].