Asymptotics of complete Kähler-Einstein metrics – negativity of the holomorphic sectional curvature.
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....
We study the singularities of plurisubharmonic functions using methods from convexity theory. Analyticity theorems for a refined Lelong number are proved.
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.
We show that proper holomorphic self maps of pseudoconvex rigid polynomial domains in C2 are automorphisms.
We show that the local automorphism group of a minimal real-analytic CR manifold is a finite dimensional Lie group if (and only if) is holomorphically nondegenerate by constructing a jet parametrization.
In questa Nota viene dato un nuovo metodo elementare per determinare il gruppo degli automorfismi del primo dominio classico. In una Nota successiva, con procedimenti del tutto analoghi verranno determinati i gruppi degli automorfismi del terzo e del quarto dominio classico.
In questa Nota vengono determinati, con un nuovo metodo elementare, i gruppi di automorfismi del terzo e del quarto dominio classico. Gli strumenti utilizzati sono quelli già introdotti nella precedente Nota, ove erano stati usati per determinare il gruppo degli automorfismi del primo dominio classico.