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 $\lvert L^{m} \rvert$ on $M$. Then the asymptotic behavior of the weights as $m \to \infty$ will be studied.