4,271 research outputs found
Geometry of free loci and factorization of noncommutative polynomials
The free singularity locus of a noncommutative polynomial f is defined to be
the sequence of hypersurfaces. The main
theorem of this article shows that f is irreducible if and only if is
eventually irreducible. A key step in the proof is an irreducibility result for
linear pencils. Apart from its consequences to factorization in a free algebra,
the paper also discusses its applications to invariant subspaces in
perturbation theory and linear matrix inequalities in real algebraic geometry.Comment: v2: 32 pages, includes a table of content
Singularity, complexity, and quasi--integrability of rational mappings
We investigate global properties of the mappings entering the description of
symmetries of integrable spin and vertex models, by exploiting their nature of
birational transformations of projective spaces. We give an algorithmic
analysis of the structure of invariants of such mappings. We discuss some
characteristic conditions for their (quasi)--integrability, and in particular
its links with their singularities (in the 2--plane). Finally, we describe some
of their properties {\it qua\/} dynamical systems, making contact with
Arnol'd's notion of complexity, and exemplify remarkable behaviours.Comment: Latex file. 17 pages. To appear in CM
Explicit description of twisted Wakimoto realizations of affine Lie algebras
In a vertex algebraic framework, we present an explicit description of the
twisted Wakimoto realizations of the affine Lie algebras in correspondence with
an arbitrary finite order automorphism and a compatible integral gradation of a
complex simple Lie algebra. This yields generalized free field realizations of
the twisted and untwisted affine Lie algebras in any gradation. The free field
form of the twisted Sugawara formula and examples are also exhibited.Comment: 24 pages, LaTeX, v2: small corrections in appendix
Stable Distributions in Stochastic Fragmentation
We investigate a class of stochastic fragmentation processes involving stable
and unstable fragments. We solve analytically for the fragment length density
and find that a generic algebraic divergence characterizes its small-size tail.
Furthermore, the entire range of acceptable values of decay exponent consistent
with the length conservation can be realized. We show that the stochastic
fragmentation process is non-self-averaging as moments exhibit significant
sample-to-sample fluctuations. Additionally, we find that the distributions of
the moments and of extremal characteristics possess an infinite set of
progressively weaker singularities.Comment: 11 pages, 5 figure
Generic features of the fluctuation dissipation relation in coarsening systems
The integrated response function in phase-ordering systems with scalar,
vector, conserved and non conserved order parameter is studied at various space
dimensionalities. Assuming scaling of the aging contribution we obtain, by numerical simulations
and analytical arguments, the phenomenological formula describing the
dimensionality dependence of in all cases considered. The primary
result is that vanishes continuously as approaches the lower
critical dimensionality . This implies that i) the existence of a non
trivial fluctuation dissipation relation and ii) the failure of the connection
between statics and dynamics are generic features of phase ordering at .Comment: 6 pages, 5 figure
Faltings heights of abelian varieties with complex multiplication
Let M be the Shimura variety associated with the group of spinor similitudes
of a rational quadratic space over of signature (n,2). We prove a conjecture of
Bruinier-Kudla-Yang, relating the arithmetic intersection multiplicities of
special divisors and big CM points on M to the central derivatives of certain
-functions. As an application of this result, we prove an averaged version
of Colmez's conjecture on the Faltings heights of CM abelian varieties.Comment: Final version. To appear in Annals of Mat
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