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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
