Slopes of smooth curves on Fano manifolds

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Ross and Thomas introduced the concept of slope stability to study K-stability, which has conjectural relation with the existence of constant scalar curvature Kahler metric. This paper presents a study of slope stability of Fano manifolds of dimension n >= 3 with respect to smooth curves. The question turns out to be easy for curves of genus at least 1 and the interest lies in the case of smooth rational curves. Our main result classifies completely the cases when a polarized Fano manifold (X, -K(X)) is not slope stable with respect to a smooth curve. Our result also states that a Fano three-fold X with Picard number 1 is slope stable with respect to every smooth curve unless X is the projective space.
Publisher
OXFORD UNIV PRESS
Issue Date
2011-10
Language
English
Article Type
Article
Keywords

KAHLER-METRICS; STABILITY

Citation

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, v.43, pp.827 - 839

ISSN
0024-6093
DOI
10.1112/blms/bdr020
URI
http://hdl.handle.net/10203/104090
Appears in Collection
MA-Journal Papers(저널논문)
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