Proceedings of the Japan Academy, Series A, Mathematical Sciences

Fano manifolds which are not slope stable along curves

Kento Fujita

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We show that a Fano manifold $(X,-K_{X})$ is \textit{not} slope stable with respect to a smooth curve $Z$ if and only if $(X,Z)$ is isomorphic to one of (projective space, line), (product of projective line and projective space, fiber of second projection) or (blow up of projective space along linear subspace of codimension two, nontrivial fiber of blow up).

Article information

Proc. Japan Acad. Ser. A Math. Sci., Volume 87, Number 10 (2011), 199-202.

First available in Project Euclid: 1 December 2011

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Zentralblatt MATH identifier

Primary: 14J45: Fano varieties 14L24: Geometric invariant theory [See also 13A50]

Fano manifold slope stability Seshadri constant


Fujita, Kento. Fano manifolds which are not slope stable along curves. Proc. Japan Acad. Ser. A Math. Sci. 87 (2011), no. 10, 199--202. doi:10.3792/pjaa.87.199.

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