2025/05/01 by Dano Kim, Xu Wang, Kim, Dano +1
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.2505.00801
openalex publication_date 2025/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In an influential L2 extension theorem due to Demailly, the finiteness of an L2 norm called the Ohsawa norm determines whether a given holomorphic function can be extended. This result has been further generalized by Zhou and Zhu to the case when the quasi-plurisubharmonic defining function of the subvariety has non-analytic singularities. We show that, however, there exist many instances of such defining functions for which only the zero function has finite Ohsawa norm, so that the L2 extension statement is void in such cases, even when it has a unique log canonical place. Such a defining function occurs already among some of the simplest non-analytic singularities, namely toric ones.