Displaying similar documents to “Projective quartics revisited”

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...

Boundedness for threefolds in P containing a smooth ruled surface as hyperplane section.

Pietro Sabatino (2005)

Revista Matemática Complutense

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Let X ⊂ P be a smooth irreducible projective threefold, and d its degree. In this paper we prove that there exists a constant β such that for all X containing a smooth ruled surface as hyperplane section and not contained in a fourfold of degree less than or equal to 15, d ≤ β. Under some more restrictive hypothesis we prove an analogous result for threefolds containing a smooth ruled surface as hyperplane section and contained in a fourfold of degree less than or equal to 15. ...

Very ampleness of multiples of principal polarization on degenerate Abelian surfaces.

Alessandro Arsie (2005)

Revista Matemática Complutense

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Quite recently, Alexeev and Nakamura proved that if Y is a stable semi-Abelic variety (SSAV) of dimension g equipped with the ample line bundle O(1), which deforms to a principally polarized Abelian variety, then O(n) is very ample as soon as n ≥ 2g + 1, that is n ≥ 5 in the case of surfaces. Here it is proved, via elementary methods of projective geometry, that in the case of surfaces this bound can be improved to n ≥ 3.

A 4₃ configuration of lines and conics in ℙ⁵

Tomasz Szemberg (1994)

Annales Polonici Mathematici

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Studying the connection between the title configuration and Kummer surfaces we write explicit quadratic equations for the latter. The main results are presented in Theorems 8 and 16.

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.

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.