On the metric structure of section rings | Vidéo | Carmin.tv

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On the metric structure of section rings

By Siarhei Finski

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

Date of recording 20/10/2022
Date of publication 16/11/2022
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

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

Domain(s)

Differential Geometry

Bibliography

FINSKI, Siarhei. On the metric structure of section ring. arXiv preprint arXiv:2209.03853, 2022. - https://doi.org/10.48550/arXiv.2209.03853
FINSKI, Siarhei. Narasimhan-Simha pseudonorms, envelopes and submultiplicative norms on section rings. arXiv preprint arXiv:2210.03039, 2022. - https://doi.org/10.48550/arXiv.2210.03039

MSC codes

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