Valuative stability of polarised varieties
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Authors
Dervan, Ruadhai
Eveline, Legendre
Publication Date
2023-02Journal Title
Mathematische Annalen
ISSN
0025-5831
Publisher
Springer
Type
Article
This Version
AM
Metadata
Show full item recordCitation
Dervan, R., & Eveline, L. (2023). Valuative stability of polarised varieties. Mathematische Annalen https://doi.org/10.1007/s00208-021-02313-4
Abstract
Fujita and Li have given a characterisation of K-stability of a Fano variety in terms of quantities associated to valuations, which has been essential to all recent progress in the area. We introduce a notion of valuative stability for arbitrary polarised varieties, and show that it is equivalent to K-stability with respect to test configurations with integral central fibre. The numerical invariant governing valuative stability is modelled on Fujita's beta invariant, but includes a term involving the derivative of the volume. We give several examples of valuatively stable and unstable varieties, including the toric case. We also discuss the role that the delta invariant plays in the study of valuative stability and K-stability of polarised varieties.
Sponsorship
Royal Society University Research Fellowship
Funder references
Royal Society (URF\R1\201041)
Identifiers
External DOI: https://doi.org/10.1007/s00208-021-02313-4
This record's URL: https://www.repository.cam.ac.uk/handle/1810/330518
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