31 research outputs found
Plurisubharmonic polynomials and bumping
We wish to study the problem of bumping outwards a pseudoconvex, finite-type
domain \Omega\subset C^n in such a way that pseudoconvexity is preserved and
such that the lowest possible orders of contact of the bumped domain with
bdy(\Omega), at the site of the bumping, are explicitly realised. Generally,
when \Omega\subset C^n, n\geq 3, the known methods lead to bumpings with high
orders of contact -- which are not explicitly known either -- at the site of
the bumping. Precise orders are known for h-extendible/semiregular domains.
This paper is motivated by certain families of non-semiregular domains in C^3.
These families are identified by the behaviour of the least-weight
plurisubharmonic polynomial in the Catlin normal form. Accordingly, we study
how to perturb certain homogeneous plurisubharmonic polynomials without
destroying plurisubharmonicity.Comment: 24 pages; corrected typos, fixed errors in Lemma 3.3; accepted for
publication in Math.
On the CR transversality of holomorphic maps into hyperquadrics
Let be a smooth Levi-nondegenerate hypersurface of signature
in with , and write for the standard
hyperquadric of the same signature in with .
Let be a holomorphic map sending into . Assume does
not send a neighborhood of in into . We show
that is necessarily CR transversal to at any point. Equivalently,
we show that is a local CR embedding from into .Comment: To appear in Abel Symposia, dedicated to Professor Yum-Tong Siu on
the occasion of his 70th birthda
Weighted integral formulas on manifolds
We present a method of finding weighted Koppelman formulas for -forms
on -dimensional complex manifolds which admit a vector bundle of rank
over , such that the diagonal of has a defining
section. We apply the method to \Pn and find weighted Koppelman formulas for
-forms with values in a line bundle over \Pn. As an application, we
look at the cohomology groups of -forms over \Pn with values in
various line bundles, and find explicit solutions to the \dbar-equation in
some of the trivial groups. We also look at cohomology groups of -forms
over \Pn \times \Pm with values in various line bundles. Finally, we apply
our method to developing weighted Koppelman formulas on Stein manifolds.Comment: 25 page
Sur les exposants de Lyapounov des applications meromorphes
Let f be a dominating meromorphic self-map of a compact Kahler manifold. We
give an inequality for the Lyapounov exponents of some ergodic measures of f
using the metric entropy and the dynamical degrees of f. We deduce the
hyperbolicity of some measures.Comment: 27 pages, paper in french, final version: to appear in Inventiones
Mat
Green Currents for Meromorphic Maps of Compact K\"ahler Manifolds
We consider the dynamics of meromorphic maps of compact K\"ahler manifolds.
In this work, our goal is to locate the non-nef locus of invariant classes and
provide necessary and sufficient conditions for existence of Green currents in
codimension one.Comment: Statement of Theorem 1.5 is slightly improved. Proposition 5.2 and
Theorem 5.3 are adde