In another paper, following an idea of R. Harvey and H. B. J. Lawson for the 1-dimensional case, the authors gave a characterization of p-K¨ahler and p-symplectic manifolds in terms of the space of positive currents which are boundaries. The proof of this theorem is based on an application of the Hahn- Banach theorem, for which they need a closure property which is trivial in the case p = 1 but requires a result which states the finite dimensionality of certain cohomology groups for p > 1; this can be obtained from a particular resolution of the sheaf of germs of real pluriharmonic functions. In this paper the authors exhibit this resolution, obtaining the required proposition. A similar resolution was considered by B. Bigolin.

A Resolution of the sheaf of Germs of Real Pluriharmonic Functions / Alessandrini, Lucia; M., Andreatta. - 92:(1986), pp. 6-13. (Intervento presentato al convegno Conference on Algebraic Geometry tenutosi a Berlin nel November 13-19, 1985).

A Resolution of the sheaf of Germs of Real Pluriharmonic Functions

ALESSANDRINI, Lucia;
1986-01-01

Abstract

In another paper, following an idea of R. Harvey and H. B. J. Lawson for the 1-dimensional case, the authors gave a characterization of p-K¨ahler and p-symplectic manifolds in terms of the space of positive currents which are boundaries. The proof of this theorem is based on an application of the Hahn- Banach theorem, for which they need a closure property which is trivial in the case p = 1 but requires a result which states the finite dimensionality of certain cohomology groups for p > 1; this can be obtained from a particular resolution of the sheaf of germs of real pluriharmonic functions. In this paper the authors exhibit this resolution, obtaining the required proposition. A similar resolution was considered by B. Bigolin.
1986
3322004163
A Resolution of the sheaf of Germs of Real Pluriharmonic Functions / Alessandrini, Lucia; M., Andreatta. - 92:(1986), pp. 6-13. (Intervento presentato al convegno Conference on Algebraic Geometry tenutosi a Berlin nel November 13-19, 1985).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2429638
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