Submultiplicative norms and filtrations on section rings

2022/10/06 by Finski, Siarhei · 2 citations
#32Q26 #32U05 #32U25 #46B28 #53C55 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2210.03039

Abstract

We show that submultiplicative norms on section rings of polarised projective manifolds are asymptotically equivalent to sup-norms associated with metrics on the polarisation. We then discuss some applications to the spectral theory of submultiplicative filtrations, the asymptotic study of the Narasimhan-Simha pseudonorms, and holomorphic extension theorem. As an unexpected byproduct, we show that injective and projective tensor norms on symmetric algebras of finite dimensional complex normed vector spaces are asymptotically equivalent.

Cited by

• Filtrations and asymptotic geometry of non-Archimedean norms on section rings
• On the Localization of the Christoffel-Darboux Kernel

Related

• On the metric structure of section ring
• Filtrations and asymptotic geometry of non-Archimedean norms on section rings
• Geometric quantization on big line bundles
• On the asymptotic tensor norm
• Projective tensor products where every element is norm-attaining