Generic coverings of plane with A-D-E-singularities

TL;DR

This paper extends previous work on the uniqueness of algebraic coverings of the plane with A-D-E singularities, establishing new bounds and proving the Chisini conjecture for certain canonical coverings of surfaces.

Contribution

It generalizes earlier results by deriving a main inequality that bounds the degree of coverings and proves the Chisini conjecture for m-canonical coverings with m≥5.

Findings

Derived a key inequality bounding the degree of coverings

Proved the Chisini conjecture for m-canonical coverings with m≥5

Analyzed fiber products of generic coverings with A-D-E singularities

Abstract

We generalize results of the paper math.AG/9803144, in which Chisini's conjecture on the unique reconstruction of f by the curve B is investigated. For this fibre products of generic coverings are studied. The main inequality bounding the degree of a covering in the case of existence of two nonequivalent coverings with the branch curve B is obtained. This inequality is used for the proof of the Chisini conjecture for m-canonical coverings of surfaces of general type for $m\ge 5$.