Explicit Hodge-type decomposition on projective complete intersections
Gennadi M. Henkin, Peter L. Polyakov
TL;DR
This paper develops an explicit homotopy formula for the d-bar complex on complete intersection subvarieties in complex projective space, providing a Hodge-type decomposition for residual currents.
Contribution
It introduces a new explicit homotopy formula for the d-bar complex on complete intersections, enabling a Hodge-type decomposition for residual currents.
Findings
Explicit homotopy formula for d-bar complex on V
Hodge-type decomposition for residual currents
Applicable to complete intersection subvarieties in CP^n
Abstract
We construct an explicit homotopy formula for the d-bar complex on a complete intersection subvariety V in CP^n. This formula can be interpreted as a Hodge-type decomposition for residual currents on V.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology · Advanced Combinatorial Mathematics