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Generalized Chisini’s conjecture. (English. Russian original) Zbl 1078.14017

Proc. Steklov Inst. Math. 241, 110-119 (2003); translation from Tr. Mat. Inst. Im. V. A. Steklova 241, 122-131 (2003).
O. Chisini’s conjecture [Ist. Lombardo Sci. Lett., Rend., Cl. Sci. Mat. Natur., III. Ser. 8(77), 339–356 (1944; Zbl 0061.35305)] claims that a generic covering of \(\mathbb{P}^2\) of degree \(\geq 5\) is determined by its branch curve. In the paper under review the author considers a generalization of this to the case of normal surfaces. This is checked in two cases: when the maximum of degrees of two generic coverings is \(\geq 2\) or when it is \(\leq 4\).
For the entire collection see [Zbl 1059.11002].

MSC:

14E20 Coverings in algebraic geometry
14E22 Ramification problems in algebraic geometry
14J17 Singularities of surfaces or higher-dimensional varieties
14H30 Coverings of curves, fundamental group

Citations:

Zbl 0061.35305
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