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Title:
Scalar Curvature and Asymptotic Chow Stability of Projective Bundles and Blowups
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Abstract:
By means of existence results of constant scalar curvature Kaehler metrics we show that a projective bundle over a smooth curve is asymptotically Chow polystable (with every polarization) if and only if the underlying bundle is slope polystable. This proves a conjecture of I. Morrison under the extra assumption that the involved polarization is sufficiently divisible. Moreover it implies that a projective bundle is asymptotically Chow polystable if and only if it admits a constant scalar curvature Kaehler metric. Finally we show how obtain new examples of asymptotically Chow unstable constant scalar curvature Kaehler surfaces by blowing up. This is a joint work with F. Zuddas.
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