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Algebraic Topology and Physics Seminar, Week 3

Alberto Della Vedova, Scalar Curvature and Asymptotic Chow Stability of Projective Bundles and Blowups


Title:
“”Scalar Curvature and Asymptotic Chow Stability of Projective Bundles and Blowups””
Speaker: Alberto Della Vedova, Princeton University
Date: Tuesday, February 7, 2012
Time: 10:30am – 11:30am
Place:Lecture Hall 102, Simons Center

 

 

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.