This article is cited in 6 scientific papers (total in 6 papers)
Isotrivial families of curves on affine surfaces and characterization of the affine plane
M. G. Zaidenberg
The main result is a characterization of $\mathbf C^2$ as a smooth acyclic algebraic surface on which there exist simply connected algebraic curves (possibly singular and reducible) or isotrivial (nonexceptional) families of curves with base $\mathbf C$. In particular, such curves and families cannot exist on Ramanujam surfaces – topologically contractible smooth algebraic surfaces not isomorphic to $\mathbf C^2$. The proof is based on a structure theorem which describes the degenerate fibers of families of curves whose geometric monodromy has finite order. Techniques of hyperbolic complex analysis are used; an important role is played by regular actions of the group $\mathbf C^*$.
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Mathematics of the USSR-Izvestiya, 1988, 30:3, 503–532
MSC: Primary 14J26, 14J25; Secondary 14D05
M. G. Zaidenberg, “Isotrivial families of curves on affine surfaces and characterization of the affine plane”, Izv. Akad. Nauk SSSR Ser. Mat., 51:3 (1987), 534–567; Math. USSR-Izv., 30:3 (1988), 503–532
Citation in format AMSBIB
\paper Isotrivial families of curves on affine surfaces and characterization of the affine plane
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\jour Math. USSR-Izv.
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