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Holomorphic Morse inequalities for orbifolds

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Abstract

We prove that Demailly’s holomorphic Morse inequalities hold true for complex orbifolds by using a heat kernel method. Then we introduce the class of Moishezon orbifolds and as an application of our inequalties, we give a geometric criterion for a compact connected orbifold to be a Moishezon orbifolds, thus generalizing Siu’s and Demailly’s answers to the Grauert–Riemenschneider conjecture to the orbifold case.

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Acknowledgements

The author thanks Xiaonan Ma and George Marinescu for helpful discussions and comments on the present paper, as well as the referee for the improvements he or she has suggested.

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  1. Institut Camille Jordan, Université Lyon 1, Bâtiment Braconnier, 43 boulevard du 11 novembre 1918, 69622, Villeurbanne cedex, France

    Martin Puchol

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  1. Martin Puchol
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Correspondence to Martin Puchol.

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This work was performed within the framework of the LABEX MILYON (ANR-10-LABX-0070) of Université de Lyon, within the program “Investissements d’Avenir” (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR).

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Puchol, M. Holomorphic Morse inequalities for orbifolds. Math. Z. 289, 1237–1260 (2018). https://doi.org/10.1007/s00209-017-1996-7

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  • DOI: https://doi.org/10.1007/s00209-017-1996-7

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