Explicit Hodge-Type Decomposition on Projective Complete Intersections

Explicit Hodge-Type Decomposition on Projective Complete Intersections

We construct an explicit homotopy formula for the ∂ ¯ -complex on a reduced complete intersection subvariety V ⊂ C 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 decompos...

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Veröffentlicht in:The Journal of Geometric Analysis 2016-01, Vol.26 (1), p.672-713
Hauptverfasser: Henkin, Gennadi M., Polyakov, Peter L.
Format: Artikel
Sprache:eng
Schlagworte:
Abstract Harmonic Analysis
Convex and Discrete Geometry
Differential Geometry
Dynamical Systems and Ergodic Theory
Fourier Analysis
Global Analysis and Analysis on Manifolds
Mathematics
Mathematics and Statistics
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Zusammenfassung:We construct an explicit homotopy formula for the ∂ ¯ -complex on a reduced complete intersection subvariety V ⊂ C 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.
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-015-9643-1