12,689 research outputs found
Iterated Monodromy Groups of Quadratic Polynomials, I
We describe the iterated monodromy groups associated with post-critically
finite quadratic polynomials, and explicit their connection to the `kneading
sequence' of the polynomial.
We then give recursive presentations by generators and relations for these
groups, and study some of their properties, like torsion and `branchness'.Comment: 18 pages, 3 EPS figure
Alternating trilinear forms on a 9-dimensional space and degenerations of (3,3)-polarized Abelian surfaces
We give a detailed analysis of the semisimple elements, in the sense of
Vinberg, of the third exterior power of a 9-dimensional vector space over an
algebraically closed field of characteristic different from 2 and 3. To a
general such element, one can naturally associate an Abelian surface X, which
is embedded in 8-dimensional projective space. We study the combinatorial
structure of this embedding and explicitly recover the genus 2 curve whose
Jacobian variety is X. We also classify the types of degenerations of X that
can occur. Taking the union over all Abelian surfaces in Heisenberg normal
form, we get a 5-dimensional variety which is a birational model for a genus 2
analogue of Shioda's modular surfaces. We find determinantal set-theoretic
equations for this variety and present some additional equations which
conjecturally generate the radical ideal.Comment: 30 pages; v2: small correction
Existence, uniqueness and a constructive solution algorithm for a class of finite Markov moment problems
We consider a class of finite Markov moment problems with arbitrary number of
positive and negative branches. We show criteria for the existence and
uniqueness of solutions, and we characterize in detail the non-unique solution
families. Moreover, we present a constructive algorithm to solve the moment
problems numerically and prove that the algorithm computes the right solution
Quantum geometry from phase space reduction
In this work we give an explicit isomorphism between the usual spin network
basis and the direct quantization of the reduced phase space of tetrahedra. The
main outcome is a formula that describes the space of SU(2) invariant states by
an integral over coherent states satisfying the closure constraint exactly, or
equivalently, as an integral over the space of classical tetrahedra. This
provides an explicit realization of theorems by Guillemin--Sternberg and Hall
that describe the commutation of quantization and reduction. In the final part
of the paper, we use our result to express the FK spin foam model as an
integral over classical tetrahedra and the asymptotics of the vertex amplitude
is determined.Comment: 33 pages, 1 figur
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Space charge induced luminescence in epoxy resin
Dielectric breakdown of epoxies is preceded by a light emission from the solid state material, so-called electroluminescence. Very little is known however on the luminescence properties of epoxy. The aim of this paper is to derive information that can be used as a basis to understand the nature of the excited states and their involvement in electrical degradation processes
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