Invariant Brauer group of an abelian variety

The Cohomological Brauer Group of a Toric Variety

Toric varieties are a special class of rational varieties defined by equations of the form monomial = monomial. For a good brief survey of the history and role of toric varieties see [10]. Any toric variety X contains a cover by affine open sets described in terms of arrangements (called fans) of convex bodies in Rr. The coordinate rings of each of these affine open sets is a graded ring genera...

On the Quotient Variety of an Abelian Variety.

Algebraic Cycles on an Abelian Variety

It is shown that to every Q-linear cycle α modulo numerical equivalence on an abelian variety A there is canonically associated a Q-linear cycle α modulo rational equivalence on A lying above α, characterised by a condition on the spaces of cycles generated by α on products of A with itself. The assignment α 7→ α respects the algebraic operations and pullback and push forward along homomorphism...

Brauer Loops and the Commuting Variety

We observe that the degree of the commuting variety and other related varieties occur as coefficients in the leading eigenvector of an integrable loop model based on the Brauer algebra.

Brauer Algebras and the Brauer Group

An algebra is a vector space V over a field k together with a kbilinear product of vectors under which V is a ring. A certain class of algebras, called Brauer algebras algebras which split over a finite Galois extension appear in many subfields of abstract algebra, including K-theory and class field theory. Beginning with a definition of the the tensor product, we define and study Brauer algebr...