Asymptotics of polybalanced metrics under relative stability constraints

TL;DR

This paper investigates the asymptotic behavior of polybalanced metrics derived from linear systems on algebraic manifolds under stability assumptions, revealing their limiting properties as the system degree grows.

Contribution

It introduces the asymptotic analysis of polybalanced metrics under relative stability constraints, expanding understanding of their behavior in complex geometry.

Findings

Weighted balanced metrics are constructed from linear systems on algebraic manifolds.

The asymptotic behavior of weights in polybalanced metrics is characterized as the degree increases.

Results connect stability conditions with metric asymptotics in algebraic geometry.

Abstract

Under the assumption of asymptotic relative Chow-stability for polarized algebraic manifolds $(M, L)$, a series of weighted balanced metrics $\omega_m$, $m \gg 1$, called polybalanced metrics, are obtained from complete linear systems $|L^m|$ on $M$. Then the asymptotic behavior of the weights as $m \to \infty$ will be studied.