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Weekly seminar of Laboratory of algebraic geometry
July 8, 2011 17:00, Moscow, Vavilova, 7
 


Kaehler-Einstein metrics, slope stability and Fano bundles

J. Park

Pohang University of Science and Technology

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Abstract: Ross and Thomas introduced the concept of slope stability to study K-stability, which has conjectural relation with the existence of constant scalar curvature Kaehler metric. My talk presents a study of slope stability of Fano manifolds of dimension $n\geq 3$ with respect to smooth curves. The question turns out to be easy for curves of genus $\geq 1$ and the interest lies in the case of smooth rational curves. I will show when a polarized Fano manifold $(X, -K_X)$ is not slope stable with respect to a smooth curve. In addition, I will show that a Fano threefold $X$ with Picard number 1 is slope stable with respect to every smooth curve unless $X$ is the projective space.

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