Spectral curves of operators with elliptic coefficients.
Eilbeck, J.Chris, Enolski, Victor Z., Previato, Emma (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Displaying similar documents to “Jacobian Nullwerte, periods and symmetric equations for hyperelliptic curves”
Spectral curves of operators with elliptic coefficients.
Finiteness results for Teichmüller curves
Martin Möller (2008)
Annales de l’institut Fourier
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We show that for each genus there are only finitely many algebraically primitive Teichmüller curves , such that (i) lies in the hyperelliptic locus and (ii) is generated by an abelian differential with two zeros of order . We prove moreover that for these Teichmüller curves the trace field of the affine group is not only totally real but cyclotomic.
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 and any finite set of places of , one can effectively compute the set of isomorphism classes of hyperelliptic curves over with good reduction outside . We show here that an extension of this result to an effective Shafarevich conjecture for of hyperelliptic curves of genus would imply an effective version of Siegel’s theorem for integral points...
About the group law for the Jacobi variety of a hyperelliptic curve.
Leitenberger, Frank (2005)
Beiträge zur Algebra und Geometrie
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The Frobenius action on rank vector bundles over curves in small genus and small characteristic
Laurent Ducrohet (2009)
Annales de l’institut Fourier
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Let be a general proper and smooth curve of genus (resp. of genus ) defined over an algebraically closed field of characteristic . When , the action of Frobenius on rank semi-stable vector bundles with trivial determinant is completely determined by its restrictions to the 30 lines (resp. the 126 Kummer surfaces) that are invariant under the action of some order line bundle over . Those lines (resp. those Kummer surfaces) are closely related to the elliptic curves (resp....
Jacobians in isogeny classes of abelian surfaces over finite fields
Everett W. Howe, Enric Nart, Christophe Ritzenthaler (2009)
Annales de l’institut Fourier
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We give a complete answer to the question of which polynomials occur as the characteristic polynomials of Frobenius for genus- curves over finite fields.