Non-upper-semicontinuity of algebraic dimension for families of compact complex manifolds

作者:Fujiki Akira*; Pontecorvo Massimiliano
来源:Mathematische Annalen, 2010, 348(3): 593-599.
DOI:10.1007/s00208-010-0492-8

摘要

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.

  • 出版日期2010-11