On the almost generic covers of the projective plane

Abstract

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 $B$.

arXiv comment13 pages. Submitted to the Pure and Applied Math. Quarterly