00:00:00 / 00:00:00

Appears in collection : Complex Geometry, Dynamical Systems and Foliation Theory / Géométrie complexe, systèmes dynamiques et théorie de feuilletages

We study the relationship between metric and algebraic structures on the section ring of a projective manifold and an ample line bundle over it. More precisely, we prove that once the kernel is factored out, the multiplication operator of the section ring becomes an approximate isometry (up to normalization) with respect to the $L^{2}$-norm. We then show that, in fact, those algebraic properties characterise $L^{2}$-norms and describe some applications of this classification. The semiclassical version of Ohsawa-Takegoshi theorem lies at the heart of our approach.

Information about the video

Citation data

  • DOI 10.24350/CIRM.V.19969303
  • Cite this video Finski, Siarhei (20/10/2022). On the metric structure of section rings. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19969303
  • URL https://dx.doi.org/10.24350/CIRM.V.19969303

Bibliography

Last related questions on MathOverflow

You have to connect your Carmin.tv account with mathoverflow to add question

Ask a question on MathOverflow




Register

  • Bookmark videos
  • Add videos to see later &
    keep your browsing history
  • Comment with the scientific
    community
  • Get notification updates
    for your favorite subjects
Give feedback