2021/04/08 by Dano Kim, Kim, Dano, Hoseob Seo +1
Mathematics · #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.2104.03554
openalex publication_date 2021/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In L2 extension theorems from a singular hypersurface in a complex manifold, important roles are played by certain measures such as the Ohsawa measure which determine when a given function can be extended. We show that the singularity of the Ohsawa measure can be identified in terms of singularity of pairs from algebraic geometry. Using this, we give an analytic proof of the inversion of adjunction in this setting. Then these considerations enable us to compare various positive and negative results on L2 extension from singular hypersurfaces. In particular, we generalize a recent negative result of Guan and Li which places limitations on strengthening such L2 extension by employing a less singular measure in the place of the Ohsawa measure.