Abstract:
It has been conjectured that if an elementary abelian group of rank r acts freely on a product of n spheres, then r is at most n.
One approach to this problem was developed by Gunnar Carlsson, who generalized the conjecture and translated the problem into commutative algebra.
We consider a variety of matrices relevant to the commutative algebra version of the conjecture and determine the components of this variety.
The results in this talk represent work of Carlsson, Oliver, Ventura, and the speaker.