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Göteborgs universitets publikationer

K-polystability of Q-Fano varieties admitting Kahler-Einstein metrics

Författare och institution:
Robert Berman (Institutionen för matematiska vetenskaper, matematik, Chalmers/GU)
Publicerad i:
Inventiones Mathematicae, 203 ( 3 ) s. 973-1025
ISSN:
0020-9910
Publikationstyp:
Artikel, refereegranskad vetenskaplig
Publiceringsår:
2016
Språk:
engelska
Fulltextlänk:
Sammanfattning (abstract):
It is shown that any, possibly singular, Fano variety X admitting a Kahler-Einstein metric is K-polystable, thus confirming one direction of the Yau-Tian-Donaldson conjecture in the setting of Q-Fano varieties equipped with their anti-canonical polarization. The proof is based on a new formula expressing the Donaldson-Futaki invariants in terms of the slope of the Ding functional along a geodesic ray in the space of all bounded positively curved metrics on the anti-canonical line bundle of X. One consequence is that a toric Fano variety X is K-polystable iff it is K-polystable along toric degenerations iff 0 is the barycenter of the canonical weight polytope P associated to X. The results also extend to the logarithmic setting and in particular to the setting of Kahler-Einsteinmetrics with edge-cone singularities. Applications to geodesic stability, bounds on the Ricci potential and Perelman's lambda-entropy functional on K-unstable Fano manifolds are also given.
Ämne (baseras på Högskoleverkets indelning av forskningsämnen):
NATURVETENSKAP ->
Matematik ->
Geometri
Nyckelord:
monge-ampere equations, scalar curvature, stable varieties, geodesic, rays, stability, bundles, manifolds, continuity, polytopes, geometry, Mathematics
Postens nummer:
235848
Posten skapad:
2016-05-03 13:56
Posten ändrad:
2016-07-01 11:34

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