Displaying similar documents to “Double covers and Calabi-Yau varieties”

On the genus of reducible surfaces and degenerations of surfaces

Alberto Calabri, Ciro Ciliberto, Flaminio Flamini, Rick Miranda (2007)

Annales de l’institut Fourier

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We deal with a reducible projective surface X with so-called , which are a generalization of normal crossings. First we compute the p ω ( X ) of X , i.e. the dimension of the vector space of global sections of the dualizing sheaf ω X . Then we prove that, when X is smoothable, i.e. when X is the central fibre of a flat family π : 𝒳 → Δ parametrized by a disc, with smooth general fibre, then the ω -genus of the fibres of π is constant.

Exceptional singular ℚ -homology planes

Karol Palka (2011)

Annales de l’institut Fourier

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We consider singular ℚ -acyclic surfaces with smooth locus of non-general type. We prove that if the singularities are topologically rational then the smooth locus is ℂ 1 - or ℂ * -ruled or the surface is up to isomorphism one of two exceptional surfaces of Kodaira dimension zero. For both exceptional surfaces the Kodaira dimension of the smooth locus is zero and the singular locus consists of a unique point of type A 1 and A 2 respectively.

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...

Fundamental groups of some special quadric arrangements.

Meirav Amram, Mina Teicher (2006)

Revista Matemática Complutense

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Continuing our work on the fundamental groups of conic-line arrangements (Amram et al., 2003), we obtain presentations of fundamental groups of the complements of three families of quadric arrangements in P. The first arrangement is a union of n conics, which are tangent to each other at two common points. The second arrangement is composed of n quadrics which are tangent to each other at one common point. The third arrangement is composed of n quadrics, n-1 of them are tangent to the...

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.

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.