On the almost generic covers of the projective plane

2018/12/04 by Kulikov, Vik. S.
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1812.01313

Abstract

A finite morphism f:X→ \mathbb P² of a a smooth irreducible projective surface X is called an almost generic cover if for each point p∈ \mathbb P² 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⊂\mathbb P² 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.

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