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A 4₃ configuration of lines and conics in ℙ⁵

Tomasz Szemberg (1994)

Annales Polonici Mathematici

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.

Around real Enriques surfaces.

Alexander Degtyarev, Vlatcheslav Kharlamov (1997)

Revista Matemática de la Universidad Complutense de Madrid

We present a brief overview of the classification of real Enriques surfaces completed recently and make an attempt to systemize the known classification results for other special types of surfaces. Emphasis is also given to the particular tools used and to the general phenomena discovered; in particular, we prove two new congruence type prohibitions on the Euler characteristic of the real part of a real algebraic surface.

Differential Equations associated to Families of Algebraic Cycles

Pedro Luis del Angel, Stefan Müller-Stach (2008)

Annales de l’institut Fourier

We develop a theory of differential equations associated to families of algebraic cycles in higher Chow groups (i.e., motivic cohomology groups). This formalism is related to inhomogenous Picard–Fuchs type differential equations. For a families of K3 surfaces the corresponding non–linear ODE turns out to be similar to Chazy’s equation.

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...

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