Liaison of product varieties

Liaison of varieties of small dimension and deficiency modules

Dominions in product varieties

Dominions, in the sense of Isbell, are investigatedin the contextof decomposable varieties of groups. An upper and lower bound for dominions in such a variety is given in terms of the two varietal factors, and the internal structure of the group being analyzed. Finally, the following result is established: If a variety N has instances of nontrivial dominions, then for any proper subvariety Q of...

Tensor Product Varieties and Crystals Ade Case

Let g be a simple simply laced Lie algebra. In this paper two families of varieties associated to the Dynkin graph of g are described: “tensor product” and “multiplicity” varieties. These varieties are closely related to Nakajima’s quiver varieties and should play an important role in the geometric constructions of tensor products and intertwining operators. In particular it is shown that the s...

Murre’s conjectures for certain product varieties

Let X be a smooth projective variety over C of dimension d. Let ∆ ⊂ X × X be the diagonal. There is a cohomology class cl(∆) ∈ H(X ×X). In this paper we use Betti cohomology with rational coefficients. There is the Künneth decomposition H(X ×X) ≃ ⊕2d i=0 H (X)⊗H (X). We write cl(∆) = ∑2d i=0 π hom i according to this decomposition. Here π hom i ∈ H (X)⊗ H (X). If the Hodge conjecture is true, t...

Maltsev Families of Varieties Closed under Join or Maltsev Product

Maltsev families of varieties which are closed under join or Maltsev product are investigated. New Maltsev conditions for congruence semi-distributivity are given.