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Versions kählériennes du théorème d'annulation de Bogomolov.

Christophe Mourougane (1998)

Collectanea Mathematica

We extend to compact Kaehler and Fujiki manifolds the theorem of F. Bogomolov, on vanishing of the space of holomorphic p-forms with values in a line bundle whose dual L is numerically effective, for the degrees p less than the numerical dimension of L.

Volume and multiplicities of real analytic sets

Guillaume Valette (2005)

Annales Polonici Mathematici

We give criteria of finite determinacy for the volume and multiplicities. Given an analytic set described by {v = 0}, we prove that the log-analytic expansion of the volume of the intersection of the set and a "little ball" is determined by that of the set defined by the Taylor expansion of v up to a certain order if the mapping v has an isolated singularity at the origin. We also compare the cardinalities of finite fibers of projections restricted to such a set.

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