In this paper we study the class of smooth complex projective varieties B such that any modular morphism B -> Mg is constant for any g>1, giving structural properties and examples. Then we investigate the concept of the moduli dimension of a variety B; we bound it by the dimension of the maximal rationally connected quotient of B. In the end, we consider also (generically smooth) families of curves of compact type over rational and elliptic curves.
Families of curves and variation in moduli
MISTRETTA, ERNESTO CARLO
2006
Abstract
In this paper we study the class of smooth complex projective varieties B such that any modular morphism B -> Mg is constant for any g>1, giving structural properties and examples. Then we investigate the concept of the moduli dimension of a variety B; we bound it by the dimension of the maximal rationally connected quotient of B. In the end, we consider also (generically smooth) families of curves of compact type over rational and elliptic curves.
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