COMPUTING GROBNER BASES AND INVARIANTS OF THE SYMMETRIC ALGEBRA

We study algebraic invariants of the symmetric algebra Sym(R)(L) of the square-free monomial ideal L = In-1 + J(n-1) in the polynomial ring R = K[X-1, ..., X-n; Y-1, ..., Y-n] where In-1 (resp. J(n-1)) is generated by all square-free monomials of degree n-1 in the variables X-1, ..., X-n (resp. Y-1, ..., Y-n). In particular, the dimension and the depth of Sym(R)(L) are investigated by techniques of Grobner bases and theory of s-sequences.