Mathematics

These are topics on determinantal ideals, based on recent collaboration with Zaqueu Ramos (UFS, Brazil).  The topics basically toss around square matrices with entries in  polynomial rings over fields, their determinants and their ideal of minors, with emphasis on submaximal and 2x2 minors. A great deal is spent in understanding special linear sections of the generic and symmetric generic matrices and a few conjectures will be posed concerning basic invariants from commutative algebra attached to both the ideals of minors, the Jacobian ideals of a determinant and the dual variety to the corresponding hypersurfaces. Overall the intent is to expose some very core questions pervasive to the commutative algebra view of determinant theory.