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Global moduli for elliptic surfaces with a section. (English) Zbl 0624.14023

Suppose that \(g\neq 0\) or \(\chi\neq 1\). Then the functor \(F_{g,\chi}\) which assigns to a \(scheme\quad T\) the collection of “all isomorphism classes of smooth families of elliptic surfaces with a section fibered over a smooth curve of genus \(g\) over T” and where \(``\chi (\vartheta)=\chi\) in all geometric fibers over T” is coarsely represented by a quasi-projective \(E_{g,\chi}\). For \((g,\chi)=(0,1)\) a subfunctor of \(F_{g,\chi}\) is represented. Questions relating to the irreducibility of \(\overline{Eg,\chi}\) receive some first step treatment.
[See also the following review.]
Reviewer: P.Cherenack

MSC:

14J10 Families, moduli, classification: algebraic theory
14D20 Algebraic moduli problems, moduli of vector bundles
32G15 Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables)
14D22 Fine and coarse moduli spaces

Citations:

Zbl 0624.14024
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References:

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