Mathematical Research Letters

Volume 25 (2018)

Number 4

Divisibilities among nodal curves

Pages: 1359 – 1368



Matthias Schütt (Institut für Algebraische Geometrie, Leibniz Universität Hannover, Germany; and Riemann Center for Geometry and Physics, Leibniz Universität, Hannover, Germany)


We prove that there are no effective or anti-effective classes of square $-1$ or $-2$ arising from nodal curves on smooth algebraic surfaces by way of divisibility. This general fact has interesting applications to Enriques and K3 surfaces. The proof relies on specific properties of root lattices and their duals.

Received 14 August 2017

Accepted 26 November 2017

Published 16 November 2018