39 research outputs found
Resonance equals reducibility for A-hypergeometric systems
Classical theorems of Gel'fand et al., and recent results of Beukers, show
that non-confluent Cohen-Macaulay A-hypergeometric systems have reducible
monodromy representation if and only if the continuous parameter is A-resonant.
We remove both the confluence and Cohen-Macaulayness conditions while
simplifying the proof.Comment: 9 pages, final versio
Variational derivation of two-component Camassa-Holm shallow water system
By a variational approach in the Lagrangian formalism, we derive the
nonlinear integrable two-component Camassa-Holm system (1). We show that the
two-component Camassa-Holm system (1) with the plus sign arises as an
approximation to the Euler equations of hydrodynamics for propagation of
irrotational shallow water waves over a flat bed. The Lagrangian used in the
variational derivation is not a metric.Comment: to appear in Appl. Ana
Off-shell superconformal nonlinear sigma-models in three dimensions
We develop superspace techniques to construct general off-shell N=1,2,3,4
superconformal sigma-models in three space-time dimensions. The most general
N=3 and N=4 superconformal sigma-models are constructed in terms of N=2 chiral
superfields. Several superspace proofs of the folklore statement that N=3
supersymmetry implies N=4 are presented both in the on-shell and off-shell
settings. We also elaborate on (super)twistor realisations for (super)manifolds
on which the three-dimensional N-extended superconformal groups act
transitively and which include Minkowski space as a subspace.Comment: 67 pages; V2: typos corrected, one reference added, version to appear
on JHE
Motives and periods in Bianchi IX gravity models
In this paper we show that the heat coefficients of the Dirac-Laplacian of SU(2)-invariant Bianchi IX metrics are periods of motives of complements in affine spaces of unions of quadrics and hyperplanes
Counting points on hyperelliptic curves over finite fields
International audienceWe describe some algorithms for computing the cardinality of hyperelliptic curves and their Jacobians over finite fields. They include several methods for obtaining the result modulo small primes and prime powers, in particular an algorithm Ă la Schoof for genus 2 using Cantor's division polynomials. These are combined with a birthday paradox algorithm to calculate the cardinality. Our methods are practical and we give actual results computed using our current implementation. The Jacobian groups we handle are larger than those previously reported in the literature
Curves over every global field violating the local-global principle
There is an algorithm that takes as input a global field k and produces a
curve over k violating the local-global principle. Also, given a global field k
and a nonnegative integer n, one can effectively construct a curve X over k
such that #X(k)=n and X has points over every completion of k.Comment: 5 page
"New" Veneziano amplitudes from "old" Fermat (hyper) surfaces
The history of discovery of bosonic string theory is well documented. This
theory evolved as an attempt to find a multidimensional analogue of Euler's
beta function. Such an analogue had in fact been known in mathematics
literature at least in 1922 and was studied subsequently by mathematicians such
as Selberg, Weil and Deligne among others. The mathematical interpretation of
this multidimensional beta function is markedly different from that described
in physics literature. This paper aims to bridge the gap between the existing
treatments. Preserving all results of conformal field theories intact,
developed formalism employing topological, algebro-geometric, number-theoretic
and combinatorial metods is aimed to provide better understanding of the
Veneziano amplitudes and, thus, of string theories.Comment: 92 pages LaTex, some typos removed, discussion section is added along
with several additional latest reference