Q-curves over quadratic fields.
Qregularity and tensor products of vector bundles on smooth quadric hypersurfaces.
Q(T)-rank of elliptic curves and certain limit coming from the local points.
Quadratic congruences on average and rational points on cubic surfaces
We investigate the average number of solutions of certain quadratic congruences. As an application, we establish Manin's conjecture for a cubic surface whose singularity type is A₅ + A₁.
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 Equations over Finite Fields and Class Numbers of Real Quadratic Fields.
Quadratic forms and singularities of genus one or two
We study singularities obtained by the contraction of the maximal divisor in compact (non-kählerian) surfaces which contain global spherical shells. These singularities are of genus 1 or 2, may be -Gorenstein, numerically Gorenstein or Gorenstein. A family of polynomials depending on the configuration of the curves computes the discriminants of the quadratic forms of these singularities. We introduce a multiplicative branch topological invariant which determines the twisting coefficient of a non-vanishing...
Quadratic forms, fibre products and some plane curves with many points
Quadratic mappings and configuration spaces
We discuss some approaches to the topological study of real quadratic mappings. Two effective methods of computing the Euler characteristics of fibers are presented which enable one to obtain comprehensive results for quadratic mappings with two-dimensional fibers. As an illustration we obtain a complete topological classification of configuration spaces of planar pentagons.
Quadratic Relations for Generators of Units in the Modular Function Field.
Quadratic twists of elliptic curves with small Selmer rank
Quadratische Formen über affinen Algebren und ein algebraischer Beweis des Satzes von Borsuk-Ulam.
Quadratische Transformationen des elliptischen Differentiales ....................unter der Voraussetzung f (x x x) = 0
Quadrics of rank four in the ideal of a canonical curve.
Quadrics through a set of points and their syzygies.
Quadro-quadric Cremona transformations in low dimensions via the -correspondence
It has been previously established that a Cremona transformation of bidegree (2,2) is linearly equivalent to the projectivization of the inverse map of a rank 3 Jordan algebra. We call this result the “-correspondence”. In this article, we apply it to the study of quadro-quadric Cremona transformations in low-dimensional projective spaces. In particular we describe new very simple families of such birational maps and obtain complete and explicit classifications in dimension 4 and 5.
Quantifier elimination, valuation property and preparation theorem in quasianalytic geometry via transformation to normal crossings
This paper investigates the geometry of the expansion of the real field ℝ by restricted quasianalytic functions. The main purpose is to establish quantifier elimination, description of definable functions by terms, the valuation property and preparation theorem (in the sense of Parusiński-Lion-Rolin). To this end, we study non-standard models of the universal diagram T of in the language ℒ augmented by the names of rational powers. Our approach makes no appeal to the Weierstrass preparation...
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”.
Quantization of Drinfeld Zastava in type
Drinfeld Zastava is a certain closure of the moduli space of maps from the projective line to the Kashiwara flag scheme of the affine Lie algebra . We introduce an affine, reduced, irreducible, normal quiver variety which maps to the Zastava space bijectively at the level of complex points. The natural Poisson structure on the Zastava space can be described on in terms of Hamiltonian reduction of a certain Poisson subvariety of the dual space of a (nonsemisimple) Lie algebra. The quantum Hamiltonian...