L² extension of holomorphic functions for log canonical pairs

2021/08/26 by Dano Kim, Kim, Dano · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2108.11934

openalex publication_date 2021/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In a general L² extension theorem of Demailly for log canonical pairs, the L² criterion with respect to a measure called the Ohsawa measure determines when a given holomorphic function can be extended. Despite the analytic nature of the Ohsawa measure, we establish a geometric characterization of this analytic criterion using the theory of log canonical centers from algebraic geometry. Along the way, we characterize when the Ohsawa measure fails to have generically smooth positive density, which answers an essential question arising from Demailly's work.

Citations

• Canonical bundle formula and degenerating families of volume forms

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