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D. D'Acunto (2000)
Annales Polonici Mathematici
We prove that the set of asymptotic critical values of a function definable in an o-minimal structure is finite, even if the structure is not polynomially bounded. As a consequence, the function is a locally trivial fibration over the complement of this set.
Francesco Amoroso (1994)
Acta Arithmetica
Victor Goryunov, David Mond (1993)
Compositio Mathematica
Yves Laurent (1993)
Inventiones mathematicae
W. Ebeling (1987)
Inventiones mathematicae
Marcos Sebastiani (1982)
Mathematische Zeitschrift
Stephen S.-T. Yau, Craig Seeley (1990)
Inventiones mathematicae
András Némethi (1996)
Banach Center Publications
B. Teissier (1977)
Inventiones mathematicae
Michel Merle (1982/1983)
Séminaire Bourbaki
Georges Dloussky, Karl Oeljeklaus (1999)
Annales de l'institut Fourier
It is well-known that minimal compact complex surfaces with containing global spherical shells are in the class VII of Kodaira. In fact, there are no other known examples. In this paper we prove that all surfaces with global spherical shells admit a singular holomorphic foliation. The existence of a numerically anticanonical divisor is a necessary condition for the existence of a global holomorphic vector field. Conversely, given the existence of a numerically anticanonical divisor, surfaces...
Adolfo Guillot (2014)
Annales de l’institut Fourier
We prove that a singular complex surface that admits a complete holomorphic vector field that has no invariant curve through a singular point of the surface is obtained from a Kato surface by contracting some divisor (in particular, it is compact). We also prove that, in a singular Stein surface endowed with a complete holomorphic vector field, a singular point of the surface where the zeros of the vector field do not accumulate is either a quasihomogeneous or a cyclic quotient singularity. We give...
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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