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Subanalytic version of Whitney's extension theorem

Krzysztof Kurdyka, Wiesław Pawłucki (1997)

Studia Mathematica

For any subanalytic C k -Whitney field (k finite), we construct its subanalytic C k -extension to n . Our method also applies to other o-minimal structures; e.g., to semialgebraic Whitney fields.

Subcanonicity of codimension two subvarieties.

Enrique Arrondo (2005)

Revista Matemática Complutense

We prove that smooth subvarieties of codimension two in Grassmannians of lines of dimension at least six are rationally numerically subcanonical. We prove the same result for smooth quadrics of dimension at least six under some extra condition. The method is quite easy, and only uses Serre s construction, Porteous formula, and Hodge index theorem.

Submersions and effective descent of étale morphisms

David Rydh (2010)

Bulletin de la Société Mathématique de France

Using the flatification by blow-up result of Raynaud and Gruson, we obtain new results for submersive and subtrusive morphisms. We show that universally subtrusive morphisms, and in particular universally open morphisms, are morphisms of effective descent for the fibered category of étale morphisms. Our results extend and supplement previous treatments on submersive morphisms by Grothendieck, Picavet and Voevodsky. Applications include the universality of geometric quotients and the elimination...

Subsheaves of the cotangent bundle

Paolo Cascini (2006)

Open Mathematics

For any smooth projective variety, we study a birational invariant, defined by Campana which depends on the Kodaira dimension of the subsheaves of the cotangent bundle of the variety and its exterior powers. We provide new bounds for a related invariant in any dimension and in particular we show that it is equal to the Kodaira dimension of the variety, in dimension up to 4, if this is not negative.

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