Pure and Applied Mathematics Quarterly

Volume 16 (2020)

Number 4

Special Issue: In Honor of Prof. Gert-Martin Greuel’s 75th Birthday

Guest Editors: Igor Burban, Stanislaw Janeczko, Gerhard Pfister, Stephen S.T. Yau, and Huaiqing Zuo

On the almost generic covers of the projective plane

Pages: 1067 – 1082

DOI: https://dx.doi.org/10.4310/PAMQ.2020.v16.n4.a7


Victor S. Kulikov (Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia)


A finite morphism $f : X \to \mathbb{P}^2$ of a a smooth irreducible projective surface $X$ is called an almost generic cover if for each point $p \in \mathbb{P}^2$ the fibre $f^{-1} (p)$ is supported at least on $\deg f - 2$ distinct points and f is ramified with multiplicity two at a generic point of its ramification locus $R$. In the article, the singular points of the branch curve $B \subset \mathbb{P}^2$ of an almost generic cover are investigated and main invariants of the covering surface $X$ are calculated in terms of invariants of the curve $B$.


covers of the projective plane, monodromy groups of covers

2010 Mathematics Subject Classification


Received 1 December 2018

Accepted 10 October 2019

Published 13 November 2020