Q-curves over quadratic fields.
Q(T)-rank of elliptic curves and certain limit coming from the local points.
Quadratic Differentials and Equivariant Deformation Theory of Curves
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...
Quadratic forms, fibre products and some plane curves with many points
Quadratic twists of elliptic curves with small Selmer rank
Quadratische Transformationen des elliptischen Differentiales ....................unter der Voraussetzung f (x x x) = 0
Quadrics of rank four in the ideal of a canonical curve.
Quantitative Riemann existence theorem over a number field
Quantization of canonical cones of algebraic curves
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”.
Quantum Singularity Theory for and -Spin Theory
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...
Quartic del Pezzo surfaces over function fields of curves
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.
Quartic surfaces with 16 skew conics.
Quasi-Frobenius-Algebren und lokal vollständige Durchschnitte.
Quasifunctions on elliptic curves over local fields.
Quasihomogene isolierte Singularitäten von Hyperflächen.
Quasihomogene Singularitäten algebraischer Kurven.
Quasi-homogeneous linear systems on ℙ² with base points of multiplicity 7, 8, 9, 10
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.
Quasi-periodic and periodic solutions of the Toda lattice via the hyperelliptic sigma function
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...
Quasipositivity and new knot invariants.
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.
Quasi-tilted algebras of canonical type