A tale of two surfaces. (English) Zbl 1388.14108

Beauville, Arnaud

Oguiso, Keiji (ed.) et al., Higher dimensional algebraic geometry. In honour of Professor Yujiro Kawamata’s sixtieth birthday. Proceedings of the conference, Tokyo, Japan, January 7–11, 2013. Tokyo: Mathematical Society of Japan (MSJ) (ISBN 978-4-86497-046-4/hbk). Advanced Studies in Pure Mathematics 74, 1-10 (2017).

Summary: We point out a link between two surfaces which have appeared recently in the literature: the surface of cuboids and the Schoen surface. Both give rise to a surface with \(q=4\), whose canonical map is 2-to-1 onto a complete intersection of 4 quadrics in \(\mathbb{P}^6\) with 48 nodes.
For the entire collection see [Zbl 1388.14012].

MSC:

14J25	Special surfaces
14J17	Singularities of surfaces or higher-dimensional varieties
14N05	Projective techniques in algebraic geometry

Keywords:

surface of cuboids; canonical map; Schoen surface