1,719,474 research outputs found
The number of maximal torsion cosets in subvarieties of tori
We present sharp bounds on the number of maximal torsion cosets in a
subvariety of the complex algebraic torus . Our
first main result gives a bound in terms of the degree of the defining
polynomials. A second result gives a bound in terms of the toric degree of the
subvariety.
As a consequence, we prove the conjectures of Ruppert and of Aliev and Smyth
on the number of isolated torsion points of a hypersurface. These conjectures
bound this number in terms of the multidegree and the volume of the Newton
polytope of a polynomial defining the hypersurface, respectively.Comment: 21 page
An Algebra of Hierarchical Graphs
We define an algebraic theory of hierarchical graphs, whose axioms characterise graph isomorphism: two terms are equated exactly when they represent the same graph. Our algebra can be understood as a high-level language for describing graphs with a node-sharing, embedding structure, and it is then well suited for defining graphical representations of software models where nesting and linking are key aspects
The Effective Bosonic Hamiltonian for Excitons Reconsidered
The effective bosonic hamiltonian for excitons, extensively quoted up to now,
cannot be correct because it is (surprisingly) non-hermitian. The oversight
physically originates from the intrinsic difficulty of properly defining
electron-hole interactions between excitons when dealing with exchange terms.
By using our commutation technique, we show that the fermionic character of the
excitons cannot be forced into a dressed Coulomb interaction only : The
effective bosonic hamiltonian must contain purely fermionic terms of the same
order as the Coulomb terms. They are necessary to ensure hermiticity, and they
do not reduce to a two-body interaction, Pauli exclusion being N-body by
essence
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