208 research outputs found
Supersolutions
We develop classical globally supersymmetric theories. As much as possible,
we treat various dimensions and various amounts of supersymmetry in a uniform
manner. We discuss theories both in components and in superspace. Throughout we
emphasize geometric aspects. The beginning chapters give a general discussion
about supersymmetric field theories; then we move on to detailed computations
of lagrangians, etc. in specific theories. An appendix details our sign
conventions. This text will appear in a two-volume work "Quantum Fields and
Strings: A Course for Mathematicians" to be published soon by the American
Mathematical Society. Some of the cross-references may be found at
http://www.math.ias.edu/~drm/QFT/Comment: 130 pages, AMSTe
On the Locus of Hodge Classes
Let be a family of non singular projective varieties
parametrized by a complex algebraic variety . Fix , an integer ,
and a class of Hodge type . We show that
the locus, on , where remains of type is algebraic. This result,
which in the geometric case would follow from the rational Hodge conjecture, is
obtained in the setting of variations of Hodge structures.Comment: 25 pages, Plain Te
Motives, Periods, and Functoriality
Given a pure motive over with a multilinear algebraic
structure on , and given a representation of the group
respecting , we describe a functorial transfer . We formulate
a criterion that guarantees when the two periods of are equal. This has
an implication for the critical values of the -function attached to
The criterion is explicated in a variety of examples such as: tensor product
motives and Rankin-Selberg -functions; orthogonal motives and the standard
-function for even orthogonal groups; twisted tensor motives and Asai
-functions
Le critère d’Abel pour la résolubilité par radicaux d’une équation irréductible de degré premier
In his last letter to Crelle, Abel states a criterion for the solvability by radicals of an irreducible equation of prime degree. Sylow finds Abel’s statement ambiguous, and writes that it should be modified. We show the correctness of Abel’s original statement
On the K(Ï€,1)-problem for restrictions of complex reflection arrangements
Let W⊂GL(V) be a complex reflection group and A(W) the set of the mirrors of the complex reflections in W. It is known that the complement X(A(W)) of the reflection arrangement A(W) is a K(π,1) space. For Y an intersection of hyperplanes in A(W), let X(A(W)Y) be the complement in Y of the hyperplanes in A(W) not containing Y. We hope that X(A(W)Y) is always a K(π,1). We prove it in case of the monomial groups W=G(r,p,ℓ). Using known results, we then show that there remain only three irreducible complex reflection groups, leading to just eight such induced arrangements for which this K(π,1) property remains to be proved
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