Open Access
June 2009 Zariski-van Kampen Method and Transcendental Lattices of Certain Singular $K3$ Surfaces
Ken-ichiro ARIMA, Ichiro SHIMADA
Tokyo J. Math. 32(1): 201-227 (June 2009). DOI: 10.3836/tjm/1249648417


We present a method of Zariski-van Kampen type for the calculation of the transcendental lattice of a complex projective surface. As an application, we calculate the transcendental lattices of complex singular $K3$ surfaces associated with an arithmetic Zariski pair of maximizing sextics of type $A_{10}+A_{9}$ that are defined over $\mathbf{Q}(\sqrt{5})$ and are conjugate to each other by the action of $\text{Gal}(\mathbf{Q}(\sqrt{5})/\mathbf{Q})$.


Download Citation

Ken-ichiro ARIMA. Ichiro SHIMADA. "Zariski-van Kampen Method and Transcendental Lattices of Certain Singular $K3$ Surfaces." Tokyo J. Math. 32 (1) 201 - 227, June 2009.


Published: June 2009
First available in Project Euclid: 7 August 2009

zbMATH: 1182.14035
MathSciNet: MR2541164
Digital Object Identifier: 10.3836/tjm/1249648417

Primary: 14J28
Secondary: 14H25 , 14H50

Rights: Copyright © 2009 Publication Committee for the Tokyo Journal of Mathematics

Vol.32 • No. 1 • June 2009
Back to Top