Hoseob Seo, On L² Extension from Singular Hypersurfaces

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. This is joint work with Dano Kim.