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Positive sheaves of differentials coming from coarse moduli spaces

Kelly Jabbusch, Stefan Kebekus (2011)

Annales de l’institut Fourier

Consider a smooth projective family of canonically polarized complex manifolds over a smooth quasi-projective complex base Y , and suppose the family is non-isotrivial. If Y is a smooth compactification of Y , such that D : = Y Y is a simple normal crossing divisor, then we can consider the sheaf of differentials with logarithmic poles along D . Viehweg and Zuo have shown that for some m > 0 , the m th symmetric power of this sheaf admits many sections. More precisely, the m th symmetric power contains an invertible...

Ramification dans le corps des modules

Stéphane Flon (2004)

Annales de l’institut Fourier

Soit f un revêtement de la droite projective défini sur ¯ , de groupe de monodromie G . Soit K le compositum des corps de rationalité des points de branchement f , et M 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 M / K des mauvaises places de f qui ne divisent pas l’ordre de G , mais où les points de branchements...

Subvarieties of the Hyperelliptic Moduli Determined by Group Actions

Shaska, T. (2006)

Serdica Mathematical Journal

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...

The moduli space of totally marked degree two rational maps

Anupam Bhatnagar (2015)

Acta Arithmetica

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 R a t t m 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 R a t t m induced from the action of SL₂ on (ℙ¹)⁵ and prove that the quotient space R a t t m / S L 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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