turkmath.org

In this talk, motivated by the algebraic version of the Carlsson's conjecture which states if k is an algebraic closure of F2, R=k[x1,…,xr] and (M, ∂) is a free, finitely generated DG-R module and its homology is nonzero, finite dimensional as a k-vector space, then the rank of M over R is at least 2r, we consider the variety of strictly upper triangular square zero 2nx2n matrices. We will describe the irreducible components of this variety and decompose into orbits of the Borel group by using Rothbach's technique. Moreover, we fix a particular irreducible component of this variety and study the structure of the subvariety of matrices of rank n in this component by using Karagueuzian, Oliver and Ventura's idea.