On the almost generic covers of the projective plane

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 $B$.

Keywords

covers of the projective plane, monodromy groups of covers

2010 Mathematics Subject Classification

14H30

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Received 1 December 2018

Accepted 10 October 2019

Published 13 November 2020