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

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Nagano A.

Acta Arithmetica

2015

tom 167

nr 4

327-345

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 of a parabola and a quintic curve in ℂ².

Ograniczanie wyników

1 Acta Arithmetica

1 Nagano A.

1 2015

Wyniki wyszukiwania

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