Asian Journal of Mathematics

Volume 22 (2018)

Number 6

New surfaces with $K^2 = 7$ and $p_g = q \leq 2$

Pages: 1117 – 1126

DOI: https://dx.doi.org/10.4310/AJM.2018.v22.n6.a7

Author

Carlos Rito (Universidade de Trás-os-Montes e Alto Douro, UTAD, Quinta de Prados, Vila Real, Portugal; and Departamento de Matemática, Faculdade de Ciências da Universidade do Porto, Portugal)

Abstract

We construct smooth minimal complex surfaces of general type with $K^2 = 7$ and: $p_g = q = 2$, Albanese map of degree $2$ onto a $(1, 2)$-polarized abelian surface; $p_g = q = 1$ as a double cover of a quartic Kummer surface; $p_g = q = 0$ as a double cover of a numerical Campedelli surface with $5$ nodes.

Keywords

surface of general type, Albanese map, double covering

2010 Mathematics Subject Classification

14J29

Full Text (PDF format)

Received 20 January 2016

Accepted 23 March 2017

Published 6 February 2019