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Double integrals on a weighted projective plane and Hilbert modular functions for ℚ (√5)

Atsuhira Nagano (2015)

Acta Arithmetica

The aim of this paper is to give an explicit extension of classical elliptic integrals to the Hilbert modular case for ℚ (√5). We study a family of Kummer surfaces corresponding to the Humbert surface of invariant 5 with two complex parameters. Our Kummer surface is given by a double covering of the weighted projective space ℙ(1:1:2) branched along a parabola and a quintic curve. The period mapping for our family is given by double integrals of an algebraic function on chambers coming from an arrangement...

Effective nonvanishing, effective global generation

Mark Andrea A. De Cataldo (1998)

Annales de l'institut Fourier

We prove a multiple-points higher-jets nonvanishing theorem by the use of local Seshadri constants. Applications are given to effectivity problems such as constructing rational and birational maps into Grassmannians, and the global generation of vector bundles.

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