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Explicit Hodge-Type Decomposition on Projective Complete Intersections

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Abstract

We construct an explicit homotopy formula for the \(\bar{\partial }\)-complex on a reduced complete intersection subvariety \(V\subset {\mathbb {C}}{\mathbb {P}}^n\). This formula can be interpreted as an explicit Hodge-type decomposition for residual currents on V. As a first application of this formula we obtained the explicit Hodge decomposition on arbitrary Riemann surfaces.

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Acknowledgments

The second author was partially supported by the NEUP program of the Department of Energy.

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Authors and Affiliations

  1. Institut de Mathematiques, Universite Pierre et Marie Curie, BC247, 75252, Paris Cedex 05, France

    Gennadi M. Henkin

  2. CEMI Acad. Sc., 117418, Moscow, Russia

    Gennadi M. Henkin

  3. Department of Mathematics, University of Wyoming, 1000 E University Ave, Laramie, WY, 82071, USA

    Peter L. Polyakov

Authors
  1. Gennadi M. Henkin
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  2. Peter L. Polyakov
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Correspondence to Peter L. Polyakov.

Additional information

To Carlos Berenstein on occasion of his 70-th birthday.

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Henkin, G.M., Polyakov, P.L. Explicit Hodge-Type Decomposition on Projective Complete Intersections. J Geom Anal 26, 672–713 (2016). https://doi.org/10.1007/s12220-015-9643-1

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  • DOI: https://doi.org/10.1007/s12220-015-9643-1

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