Canonical coordinates and Bergman metrics
نویسنده
چکیده
In this paper we will discuss local coordinates canonically corresponding to a Kähler metric. We will also discuss the C ∞ convergence of Bergman metrics following Tian's result on C 2 convergence of Bergman metrics. At the end we present an interesting characterization of ample line bundle that could be useful in arithmetic geometry.
منابع مشابه
Double Integral Characterization for Bergman Spaces
‎In this paper we characterize Bergman spaces with‎ ‎respect to double integral of the functions $|f(z)‎ ‎-f(w)|/|z-w|$,‎ ‎$|f(z)‎ -‎f(w)|/rho(z,w)$ and $|f(z)‎ ‎-f(w)|/beta(z,w)$,‎ ‎where $rho$ and $beta$ are the pseudo-hyperbolic and hyperbolic metrics‎. ‎We prove some necessary and sufficient conditions that implies a function to be...
متن کامل0 O ct 1 99 6 Canonical coordinates and Bergmann metrics
In this paper we will discuss local coordinates canonically corresponding to a Kähler metric. We will also discuss the C ∞ convergence of Bergmann metrics following Tian's result on C 2 convergence of Bergmann metrics. At the end we present an interesting characterization of ample line bundle that could be useful in arithmetic geometry.
متن کاملCaculus of Variation and the L-Bergman Metric on Teichmüller Space
The canonical metric on a surface is of nonpositive curvature, so it is natural to study harmonic maps between canonical metrics on a surface in a fixed homotopy class. Through this approach, we establish the LBergman metric on Teichmüller space as the second variation of energy functionals of chosen families of harmonic maps.
متن کاملCanonical form of linear subspaces and coding invariants: the poset metric point of view
In this work we introduce the concept of a sub-space decomposition, subject to a partition of the coordinates. Considering metrics determined by partial orders in the set of coordinates, the so called poset metrics, we show the existence of maximal decompositions according to the metric. These decompositions turns to be an important tool to obtain the canonical form for codes over any poset met...
متن کاملConvergence of Bergman geodesics on CP1
This article is concerned with geodesics in spaces of Hermitian metrics of positive curvature on an ample line bundle L → X over a Kähler manifold. Stimulated by a recent article of Phong-Sturm [PS], we study the convergence as N → ∞ of geodesics on the finite dimensional symmetric spaces HN of Bergman metrics of ‘height N ’ to Monge-Ampére geodesics on the full infinite dimensional symmetric s...
متن کامل