Displaying similar documents to “Belyi's theorem revisited.”

Field of moduli versus field of definition for cyclic covers of the projective line

Aristides Kontogeorgis (2009)

Journal de Théorie des Nombres de Bordeaux

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We give a criterion, based on the automorphism group, for certain cyclic covers of the projective line to be defined over their field of moduli. An example of a cyclic cover of the complex projective line with field of moduli ℝ that can not be defined over ℝ is also given.

On the Nagata automorphism.

Spodzieja, Stanisław (2007)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

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Triviality of scalar linear type isotropy subgroup by passing to an alternative canonical form of a hypersurface

Vladimir V. Ežov (1998)

Annales Polonici Mathematici

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The Chern-Moser (CM) normal form of a real hypersurface in ℂ N can be obtained by considering automorphisms whose derivative acts as the identity on the complex tangent space. However, the CM normal form is also invariant under a larger group (pseudo-unitary linear transformations) and it is this property that makes the CM normal form special. Without this additional restriction, various types of normal forms occur. One of them helps to give a simple proof of a (previously complicated)...

On elementary equivalence, isomorphism and isogeny

Pete L. Clark (2006)

Journal de Théorie des Nombres de Bordeaux

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Motivated by recent work of Florian Pop, we study the connections between three notions of equivalence of function fields: isomorphism, elementary equivalence, and the condition that each of a pair of fields can be embedded in the other, which we call isogeny. Some of our results are purely geometric: we give an isogeny classification of Severi-Brauer varieties and quadric surfaces. These results are applied to deduce new instances of “elementary equivalence implies isomorphism”: for...

Siegel’s theorem and the Shafarevich conjecture

Aaron Levin (2012)

Journal de Théorie des Nombres de Bordeaux

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It is known that in the case of hyperelliptic curves the Shafarevich conjecture can be made effective, i.e., for any number field k and any finite set of places S of k , one can effectively compute the set of isomorphism classes of hyperelliptic curves over k with good reduction outside S . We show here that an extension of this result to an effective Shafarevich conjecture for of hyperelliptic curves of genus g would imply an effective version of Siegel’s theorem for integral points...