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Displaying similar documents to “Boundedness for threefolds in P6 containing a smooth ruled surface as hyperplane section.”

Projective quartics revisited

T. Szemberg, H. Tutaj-Gasińska (1999)

Annales Polonici Mathematici

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We classify all smooth projective varieties of degree 4 and describe their syzygies.

Subcanonicity of codimension two subvarieties.

Enrique Arrondo (2005)

Revista Matemática Complutense

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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.

On the extendability of elliptic surfaces of rank two and higher

Angelo Felice Lopez, Roberto Muñoz, José Carlos Sierra (2009)

Annales de l’institut Fourier

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We study threefolds X ⊂ ℙ r having as hyperplane section a smooth surface with an elliptic fibration. We first give a general theorem about the possible embeddings of such surfaces with Picard number two. More precise results are then proved for Weierstrass fibrations, both of rank two and higher. In particular we prove that a Weierstrass fibration of rank two that is not a K3 surface is not hyperplane section of a locally complete intersection threefold and we give some conditions, for many...

A family of varieties with exactly one pointless rational fiber

Bianca Viray (2010)

Journal de Théorie des Nombres de Bordeaux

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We construct a concrete example of a 1 -parameter family of smooth projective geometrically integral varieties over an open subscheme of ℙ ℚ 1 such that there is exactly one rational fiber with no rational points. This makes explicit a construction of Poonen.