In this note we show that in a certain subfamily of the Kuranishi family of any half Inoue surface the algebraic dimensions of the fibers jump downwards at special points of the parameter space showing that the upper semicontinuity of algebraic dimensions in any sense does not hold in general for families of compact non-K hler manifolds. In the K hler case, the upper semicontinuity always holds true in a certain weak sense. -
A., F., Pontecorvo, M. (2010). Non-upper-semicontinuity of algebraic dimension for families of compact complex manifolds. MATHEMATISCHE ANNALEN, 348, 593-599 [10.1007/s00208-010-0492-8].
Non-upper-semicontinuity of algebraic dimension for families of compact complex manifolds
PONTECORVO, Massimiliano
2010-01-01
Abstract
In this note we show that in a certain subfamily of the Kuranishi family of any half Inoue surface the algebraic dimensions of the fibers jump downwards at special points of the parameter space showing that the upper semicontinuity of algebraic dimensions in any sense does not hold in general for families of compact non-K hler manifolds. In the K hler case, the upper semicontinuity always holds true in a certain weak sense. -File in questo prodotto:
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