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A Note on Chow Stability of the Projectivization of Gieseker Stable Bundles

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Abstract

We investigate Chow stability of projective bundles ℙ(E), where E is a strictly Gieseker stable bundle over a base manifold that has constant scalar curvature. We show that, for suitable polarizations \(\mathcal{L}\), the pair \((\mathbb{P}(E),\mathcal{L})\) is Chow stable and give examples for which it is not asymptotically Chow stable.

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Notes

  1. This corrects an error in the lower order term of [24, Proposition 5.23].

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Acknowledgements

This research was supported by a Marie Curie International Reintegration Grant within the 7th European Community Framework Programme and the French Agence Nationale de la Recherche—ANR project MNGNK (ANR-10-BLAN-0118).

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Authors and Affiliations

  1. University of Provence, Marseille, France

    Julien Keller

  2. DPMMS, University of Cambridge, Cambridge, UK

    Julius Ross

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  1. Julien Keller
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  2. Julius Ross
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Correspondence to Julius Ross.

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Communicated by Bo Berndtsson.

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Keller, J., Ross, J. A Note on Chow Stability of the Projectivization of Gieseker Stable Bundles. J Geom Anal 24, 1526–1546 (2014). https://doi.org/10.1007/s12220-012-9384-3

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