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SHARP BOUNDS ON THE HEIGHT OF K-SEMISTABLE FANO VARIETIES II, THE LOG CASE

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Názov: SHARP BOUNDS ON THE HEIGHT OF K-SEMISTABLE FANO VARIETIES II, THE LOG CASE
Autori: Andreasson, Rolf, 1997, Berman, Robert, 1976
Zdroj: Journal de l'Ecole Polytechnique - Mathematiques. 12:983-1018
Predmety: heights, Fano varieties, Arakelov geometry, hler-Einstein metrics, K-stability, K & auml
Popis: In our previous work we conjectured-inspired by an algebro-geometric result of Fujita-that the height of an arithmetic Fano variety X of relative dimension n is maximal when X is the projective space lln Z over the integers, endowed with the Fubini-Study metric, if the corresponding complex Fano variety is K-semistable. In this work the conjecture is settled for diagonal hypersurfaces in lln+1 Z . The proof is based on a logarithmic extension of our previous conjecture, of independent interest, which is established for toric log Fano varieties of relative dimension at most three, hyperplane arrangements on lln Z, as well as for general arithmetic orbifold Fano surfaces.
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Prístupová URL adresa: https://research.chalmers.se/publication/547509
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  Data: SHARP BOUNDS ON THE HEIGHT OF K-SEMISTABLE FANO VARIETIES II, THE LOG CASE
– Name: Author
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  Data: <searchLink fieldCode="AR" term="%22Andreasson%2C+Rolf%22">Andreasson, Rolf</searchLink>, 1997<br /><searchLink fieldCode="AR" term="%22Berman%2C+Robert%22">Berman, Robert</searchLink>, 1976
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  Data: <i>Journal de l'Ecole Polytechnique - Mathematiques</i>. 12:983-1018
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  Data: <searchLink fieldCode="DE" term="%22heights%22">heights</searchLink><br /><searchLink fieldCode="DE" term="%22Fano+varieties%22">Fano varieties</searchLink><br /><searchLink fieldCode="DE" term="%22Arakelov+geometry%22">Arakelov geometry</searchLink><br /><searchLink fieldCode="DE" term="%22hler-Einstein+metrics%22">hler-Einstein metrics</searchLink><br /><searchLink fieldCode="DE" term="%22K-stability%22">K-stability</searchLink><br /><searchLink fieldCode="DE" term="%22K+%26+auml%22">K & auml</searchLink>
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  Data: In our previous work we conjectured-inspired by an algebro-geometric result of Fujita-that the height of an arithmetic Fano variety X of relative dimension n is maximal when X is the projective space lln Z over the integers, endowed with the Fubini-Study metric, if the corresponding complex Fano variety is K-semistable. In this work the conjecture is settled for diagonal hypersurfaces in lln+1 Z . The proof is based on a logarithmic extension of our previous conjecture, of independent interest, which is established for toric log Fano varieties of relative dimension at most three, hyperplane arrangements on lln Z, as well as for general arithmetic orbifold Fano surfaces.
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      – SubjectFull: Fano varieties
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      – SubjectFull: Arakelov geometry
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      – SubjectFull: K & auml
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              Y: 2025
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