Q-curves over quadratic fields.
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Yuji Hasegawa (1997)
Manuscripta mathematica
Koh-ichi Nagao (1997)
Manuscripta mathematica
Bernhard Köck, Aristides Kontogeorgis (2012)
Annales de l’institut Fourier
Given a finite -group acting on a smooth projective curve over an algebraically closed field of characteristic , the dimension of the tangent space of the associated equivariant deformation functor is equal to the dimension of the space of coinvariants of acting on the space of global holomorphic quadratic differentials on . We apply known results about the Galois module structure of Riemann-Roch spaces to compute this dimension when is cyclic or when the action of on is weakly...
Motoko Qiu Kawakita, Shinji Miura (2002)
Acta Arithmetica
Sungkon Chang (2010)
Acta Arithmetica
Gundelfeiger (1874)
Mathematische Annalen
M.L. Green (1984)
Inventiones mathematicae
Yuri F. Bilu, Marco Strambi (2010)
Acta Arithmetica
Benjamin Enriquez, Alexander Odesskii (2002)
Annales de l’institut Fourier
We introduce a quantization of the graded algebra of functions on the canonical cone of an algebraic curve , based on the theory of formal pseudodifferential operators. When is a complex curve with Poincaré uniformization, we propose another, equivalent construction, based on the work of Cohen-Manin-Zagier on Rankin-Cohen brackets. We give a presentation of the quantum algebra when is a rational curve, and discuss the problem of constructing algebraically “differential liftings”.
Huijun Fan, Tyler Jarvis, Yongbin Ruan (2011)
Annales de l’institut Fourier
We give a review of our construction of a cohomological field theory for quasi-homogeneous singularities and the -spin theory of Jarvis-Kimura-Vaintrob. We further prove that for a singularity of type our construction of the stack of -curves is canonically isomorphic to the stack of -spin curves described by Abramovich and Jarvis. We further prove that our theory satisfies all the Jarvis-Kimura-Vaintrob axioms for an -spin virtual class. Therefore, the Faber-Shadrin-Zvonkine proof of the...
Brendan Hassett, Yuri Tschinkel (2014)
Open Mathematics
We classify quartic del Pezzo surface fibrations over the projective line via numerical invariants, giving explicit examples for small values of the invariants. For generic such fibrations, we describe explicitly the geometry of spaces of sections to the fibration, and mappings to the intermediate Jacobian of the total space. We exhibit examples where these are birational, which has applications to arithmetic questions, especially over finite fields.
Th. Bauer (1995)
Journal für die reine und angewandte Mathematik
Günter Scheja, Uwe Storch (1976)
Manuscripta mathematica
Horst G. Zimmer (1979)
Journal für die reine und angewandte Mathematik
Kyoji Saito (1971)
Inventiones mathematicae
Ernst Kunz, Walter Ruppert (1977)
Manuscripta mathematica
Marcin Dumnicki (2011)
Annales Polonici Mathematici
We prove that the Segre-Gimigliano-Harbourne-Hirschowitz conjecture holds for quasi-homogeneous linear systems on ℙ² for m = 7, 8, 9, 10, i.e. systems of curves of a given degree passing through points in general position with multiplicities at least m,...,m,m₀, where m = 7, 8, 9, 10, m₀ is arbitrary.
Yuji Kodama, Shigeki Matsutani, Emma Previato (2013)
Annales de l’institut Fourier
A lattice model with exponential interaction, was proposed and integrated by M. Toda in the 1960s; it was then extensively studied as one of the completely integrable (differential-difference) equations by algebro-geometric methods, which produced both quasi-periodic solutions in terms of theta functions of hyperelliptic curves and periodic solutions defined on suitable Jacobians by the Lax-pair method. In this work, we revisit Toda’s original approach to give solutions of the Toda lattice in terms...
Lee Rudolph (1989)
Revista Matemática de la Universidad Complutense de Madrid
This is a survey (including new results) of relations ?some emergent, others established? among three notions which the 1980s saw introduced into knot theory: quasipositivity of a link, the enhanced Milnor number of a fibered link, and the new link polynomials. The Seifert form fails to determine these invariants; perhaps there exists an ?enhanced Seifert form? which does.
Helmut Lenzing, Andrzej Skowroński (1996)
Colloquium Mathematicae
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