Asymptotics of polybalanced metrics under relative stability constraints

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.

to appear in Osaka J. Math

References in corpus (2)

• An energy-theoretic approach to the Hitchin-Kobayashi correspondence for manifolds, II
• K-stability of constant scalar curvature polarization