Chisini's conjecture on generic coverings of the projective plane
Let be a cuspidal branch curve, and let
be generic coverings of degree at least , meaning that their branch curve has only nodes and cusps and the local monodromy at a smooth point of the branch curve is a transposition. Two such coverings are equivalent when they are equivalent as coverings of .
Chisini's conjecture. Given two generic coverings and , both of degree at least , with the same branch curve , the coverings and are equivalent.
The conjecture asks whether a generic covering of degree at least is determined by its branch curve. The supplied text gives no resolution or qualification of its status.
References
Primary source
Fabrizio Catanese, “Differentiable and deformation type of algebraic surfaces, real and symplectic structures”, arXiv:0705.1522 (2007).
Additional references
4 papers in this index state this conjecture (1998–2007). The statement above is taken from the most recent of them; the others are arXiv:math/9807154, arXiv:math/9807153, arXiv:math/9803144.
Progress summary
Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.
Solutions 0
No solutions have been posted yet.