On toric geometry and K-stability of Fano varieties
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- by Anne-Sophie Kaloghiros and Andrea Petracci HTML | PDF
- Trans. Amer. Math. Soc. Ser. B 8 (2021), 548-577
Abstract:
We present some applications of the deformation theory of toric Fano varieties to K-(semi/poly)stability of Fano varieties. First, we present two examples of K-polystable toric Fano $3$-fold with obstructed deformations. In one case, the K-moduli spaces and stacks are reducible near the closed point associated to the toric Fano $3$-fold, while in the other they are non-reduced near the closed point associated to the toric Fano $3$-fold. Second, we study K-stability of the general members of two deformation families of smooth Fano $3$-folds by building degenerations to K-polystable toric Fano $3$-folds.References
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Additional Information
- Anne-Sophie Kaloghiros
- Affiliation: Department of Mathematics, Brunel University London, Kingston Lane, Uxbridge UB8 3PH, United Kingdom
- MR Author ID: 912655
- ORCID: 0000-0002-8305-8229
- Email: anne-sophie.kaloghiros@brunel.ac.uk
- Andrea Petracci
- Affiliation: Institut für Mathematik, Freie Universität Berlin, Arnimallee 3, Berlin 14195, Germany
- MR Author ID: 1138308
- ORCID: 0000-0003-4837-3431
- Email: andrea.petracci@fu-berlin.de
- Received by editor(s): October 10, 2020
- Received by editor(s) in revised form: May 3, 2021
- Published electronically: July 16, 2021
- Additional Notes: The first author’s research was supported by Engineering and Physical Sciences Research Council Grant EP/P029949/1
- © Copyright 2021 by the authors under Creative Commons Attribution 3.0 License (CC BY 3.0)
- Journal: Trans. Amer. Math. Soc. Ser. B 8 (2021), 548-577
- MSC (2020): Primary 14J45, 14M25, 14B07, 14D23
- DOI: https://doi.org/10.1090/btran/82
- MathSciNet review: 4287508