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Stefano Trapani

Publications and source records attributed to Stefano Trapani.

23 records · Page 2Linked to original sources
arXiv2010

A remark on the codimension of the Green-Griffiths locus of generic projective hypersurfaces of high degree

We show that for every smooth generic projective hypersurface $X\subset\mathbb P^{n+1}$, there exists a proper subvariety $Y\subsetneq X$ such that $\operatorname{codim}_X Y\ge 2$ and for every non constant holomorphic entire map $f\colon\mathbb C\to X$ one has $f(\mathbb C)\subset Y$, provided $°X\ge 2^{n^5}$. In particular, we obtain an effective confirmation of the Kobayashi conjecture for threefolds in $\mathbb P^4$.

math.CV↗
arXiv2005

The pluricomplex Poisson kernel for strongly convex domains

Let $D$ be a bounded strongly convex domain in the complex space of dimension $n$. Fixed a point $p\in \partial D$, we consider the solution of a homogeneous complex Monge-Ampere equation with simple pole at $p$. We prove that such a solution enjoys many properties of the classical Poisson kernel in the unit disc and thus deserves to be called the pluricomplex Poisson kernel of $D$ with pole at $p$. In particular we discuss extremality properties (such as a generalization of the classical Phragmen-Lindelof theorem), relations with the pluricomplex Green function of $D$, uniqueness in terms of the associated foliation and boundary behaviors and reproducing formulas for plurisubharmonic functions.

math.CV↗
arXiv1996

Defect and evaluations

Let $S$ be a generic submanifold of $C^N$ of real codimension m. In this work we continue the study, carried over by various authors, of the set of analytic discs attached to S. Let $M$ be the set of analytic discs attached to $S.$ Given $q \in S$ let $M_q$ be the set of discs $ϕ$ in M such that $ϕ_(1).$ B. Trepreau and other authors gave sufficient conditions for $M$ to be a manifold in a neighborhood of a given disc. We give conditions for $M_q$ to be a manifold. When this conditions are satisfied we look at the map on $M$ given by $ϕ\rightarrow ϕ(0),$ and we describe the image of its differential, (in particular we determine its dimension). We then do the same for the map $ϕ\rightarrow ϕ(-1)$ on $M_q.$ For example we find as a corollary that if S has only minimal points, then there exists an open dense subset $Omega$ in M such that the restriction of the map $ϕ\rightarrow ϕ(0)$ to $Ω$ is an open map with value in $C^N.$

math.CV↗