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Some Remarks About Chow, Hilbert and K-stability of Ruled Threefolds

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Current Trends in Analysis and Its Applications

Part of the book series: Trends in Mathematics ((RESPERSP))

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Abstract

Given a rank 2 holomorphic vector bundle E over a projective surface, we explain some relationships between the Gieseker stability of E and the Chow, Hilbert and K-stability of the polarized ruled manifold \(\mathbb{P}E\) with respect to polarizations that make fibres sufficiently small.

This work was completed with the support of the French Agence Nationale de la Recherche—ANR project MNGNK (ANR-10-BLAN-0118).

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Acknowledgements

I want to thank J. Ross, R. Seyyedali, J. Stoppa and X. Wang for interesting conversations on the subject throughout the years. I am also grateful to Professor Alexander Schmitt and the organizers of International ISAAC Congress for their invitation and hospitality.

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Authors and Affiliations

  1. Centre Mathématiques et Informatique, I2M, Aix-Marseille University, 39 rue F. Joliot-Curie, 13453, Marseille Cedex 13, France

    Julien Keller

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  1. Julien Keller
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Correspondence to Julien Keller .

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Editors and Affiliations

  1. Dept. of Computer Sc. & Comp. Methods, Pedagogical University, Kraków, Poland

    Vladimir V. Mityushev

  2. Imperial College London, London, United Kingdom

    Michael V. Ruzhansky

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Keller, J. (2015). Some Remarks About Chow, Hilbert and K-stability of Ruled Threefolds. In: Mityushev, V., Ruzhansky, M. (eds) Current Trends in Analysis and Its Applications. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-12577-0_42

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