Asymptotic behaviors of complex analytic dynamical systems.
Asymptotic behaviour of numerical invariants of algebraic varieties
We show that if the degree of a nonsingular projective variety is high enough, maximization of any of the most important numerical invariants, such as class, Betti number, and any of the Chern or middle Hodge numbers, leads to the same class of extremal varieties. Moreover, asymptotically (say, for varieties whose total Betti number is big enough) the ratio of any two of these invariants tends to a well-defined constant.
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 Curves on Real Analytic Surfaces in C2.
Asymptotic expansion of the Bergman kernel for weakly pseudoconvex tube domains in
Asymptotic Morse inequalities for analytic sheaf cohomology
Asymptotic Morse inequalities for pseudoconcave manifolds
Asymptotics for Bergman kernels for high powers of complex line bundles, based on joint works with B. Berndtsson and R. Berman
Nous discutons l’asymptotique des noyaux de Bergman pour des puissances élevées de fibrés de droites, d’après deux travaux récents avec B.Berndtsson et R. Berman.
Asymptotics for Bergman-Hodge kernels for high powers of complex line bundles
In this paper we obtain the full asymptotic expansion of the Bergman-Hodge kernel associated to a high power of a holomorphic line bundle with non-degenerate curvature. We also explore some relations with asymptotic holomorphic sections on symplectic manifolds.
Asymptotics of complete Kähler-Einstein metrics – negativity of the holomorphic sectional curvature.
Asymptotics of eigensections on toric varieties
Using exhaustion properties of invariant plurisubharmonic functions along with basic combinatorial information on toric varieties, we prove convergence results for sequences of densities for eigensections approaching a semiclassical ray. Here is a normal compact toric variety and is an ample line bundle equipped with an arbitrary positive bundle metric which is invariant with respect to the compact form of the torus. Our work was motivated by and extends that of Shiffman, Tate and Zelditch....
Asymptotics of holomorphic sections of powers of a positive line bundle
Asymptotics of Matrix Coefficients, Perverse Sheaves and Jacquet Modules.
Asymptotique des intégrales-fibres
Athe ...-Neumann Operator on the Unit Ball in Cn.
Attenuating the singularities of plurisubharmonic functions
We study the singularities of plurisubharmonic functions using methods from convexity theory. Analyticity theorems for a refined Lelong number are proved.
Attracting divisors on projective algebraic varieties
We obtain sufficient and necessary conditions (in terms of positive singular metrics on an associated line bundle) for a positive divisor D on a projective algebraic variety X to be attracting for a holomorphic map f:X → X.
Attraction des disques analytiques et continuité Höldérienne d'applications holomorphes propres
Auflösung der Entartungen holomorpher Abbildungen zwischen zweidimensionalen Mannigfaltigkeiten.
Auto-applications holomorphes propies des domaines polynomiaux rigides de C2.
We show that proper holomorphic self maps of pseudoconvex rigid polynomial domains in C2 are automorphisms.