In this paper, we consider a proper modification (Formula presented.) between complex manifolds, and study when a generalized p-Kähler property goes back from M to (Formula presented.). When f is the blow-up at a point, every generalized p-Kähler property is conserved, while when f is the blow-up along a submanifold, the same is true for (Formula presented.). For (Formula presented.), we prove that the class of compact generalized balanced manifolds is closed with respect to modifications, and we show that the fundamental forms can be chosen in the expected cohomology class. We also get some partial results in the non-compact case; finally, we end the paper with some examples of generalized p-Kähler manifolds.

Proper Modifications of Generalized p-Kähler Manifolds / Alessandrini, Lucia. - In: THE JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1050-6926. - 27:2(2017), pp. 947-967. [10.1007/s12220-016-9705-z]

Proper Modifications of Generalized p-Kähler Manifolds

ALESSANDRINI, Lucia
2017-01-01

Abstract

In this paper, we consider a proper modification (Formula presented.) between complex manifolds, and study when a generalized p-Kähler property goes back from M to (Formula presented.). When f is the blow-up at a point, every generalized p-Kähler property is conserved, while when f is the blow-up along a submanifold, the same is true for (Formula presented.). For (Formula presented.), we prove that the class of compact generalized balanced manifolds is closed with respect to modifications, and we show that the fundamental forms can be chosen in the expected cohomology class. We also get some partial results in the non-compact case; finally, we end the paper with some examples of generalized p-Kähler manifolds.
Proper Modifications of Generalized p-Kähler Manifolds / Alessandrini, Lucia. - In: THE JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1050-6926. - 27:2(2017), pp. 947-967. [10.1007/s12220-016-9705-z]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2815111
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