Problem 24.10.1D2B2B955B9A6

Problem 24.10.1.D2B2B955B9A6 Let $L\to X$ be a holomorphic line bundle with a smooth Hermitian metric, and consider a series of selected spaces of sections of $L^ m$ with weighted $L^2$ norms, as in section 18.30, together with its intrinsic growth dimension. Identify hypotheses on the series under which the partial Fubini–Study potentials attain the lower bound given by the envelope and the kernel measures, normalized in the growth dimension, converge. Relate the limiting measure to the Hermitian background while keeping track of the closed curvature and of the growth dimension of the series.