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Consider a smooth projective family of canonically polarized complex manifolds over a smooth quasi-projective complex base , and suppose the family is non-isotrivial. If is a smooth compactification of , such that is a simple normal crossing divisor, then we can consider the sheaf of differentials with logarithmic poles along . Viehweg and Zuo have shown that for some , the symmetric power of this sheaf admits many sections. More precisely, the symmetric power contains an invertible...
Soit un revêtement de la droite projective défini sur , de groupe
de monodromie . Soit le compositum des corps de rationalité des points de
branchement , et le corps des modules correspondants. Partant du lien entre corps
des modules et espaces de Hurwitz, on étudie la géométrie et l’arithmétique de ces
espaces et des espaces de configuration de points complétés pour évaluer la ramification
dans des mauvaises places de qui ne divisent pas l’ordre de , mais où les
points de branchements...
For some values of the degrees of the equations, we show, using geometric invariant theory, that the coarse moduli space of smooth complete intersections in is quasi-projective.
2000 Mathematics Subject Classification: 14Q05, 14Q15, 14R20, 14D22.Let Hg be the moduli space of genus g hyperelliptic curves. In this note, we study the locus Hg (G,σ) in Hg of curves admitting a G-action of given ramification type σ and inclusions between such loci. For each genus we determine the list of all possible groups, the inclusions among the loci, and the corresponding equations of the generic curve in Hg (G, σ). The proof of the results is based solely on representations of finite subgroups...
A rational map ϕ: ℙ¹ → ℙ¹ along with an ordered list of fixed and critical points is called a totally marked rational map. The space of totally marked degree two rational maps can be parametrized by an affine open subset of (ℙ¹)⁵. We consider the natural action of SL₂ on induced from the action of SL₂ on (ℙ¹)⁵ and prove that the quotient space exists as a scheme. The quotient is isomorphic to a Del Pezzo surface with the isomorphism being defined over ℤ[1/2].
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