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Multiplier ideal sheaves and integral invariants on toric Fano manifolds

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Abstract

We extend Nadel’s results on some conditions for the multiplier ideal sheaves to satisfy which are described in terms of an obstruction defined by the first author. Applying our extension we can determine the multiplier ideal subvarieties on toric del Pezzo surfaces which do not admit Kähler–Einstein metrics. We also show that one can define multiplier ideal sheaves for Kähler–Ricci solitons and extend the result of Nadel using the holomorphic invariant defined by Tian and Zhu.

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Authors and Affiliations

  1. Department of Mathematics, Tokyo Institute of Technology, 2-12-1, O-okayama, Meguro, Tokyo, 152-8551, Japan

    Akito Futaki

  2. Institut des Hautes Études Scientifiques, Le Bois-Marie, 35, route de Chatres, 91440, Bures-sur-Yvette, France

    Yuji Sano

Authors
  1. Akito Futaki
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  2. Yuji Sano
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Correspondence to Akito Futaki.

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Futaki, A., Sano, Y. Multiplier ideal sheaves and integral invariants on toric Fano manifolds. Math. Ann. 350, 245–267 (2011). https://doi.org/10.1007/s00208-010-0556-9

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  • DOI: https://doi.org/10.1007/s00208-010-0556-9

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