We classify the tangential varieties of Segre–Veronese which are Cohen–Macaulay or Gorenstein.

We settle the negativity conjecture of Vasconcelos for the Chern number of an ideal in certain unmixed quotients of regular local rings by explicit calculation of the Hilbert polynomials of all ideals generated by systems of parameters. Introduction Let I be an m-primary ideal in a local ring (R,m) of dimension d. Let H(I, n) = λ(R/I) denote the Hilbert function of I where λ(M) denotes the leng...

This paper shows that Cohen-Macaulay algebras can be algebraically approximated in such a way their Cohen-Macaulayness and minimal Betti numbers are preserved. is achieved by showing finitely generated modules over power series rings manner preserves diagrams of initial exponents numbers. These results also applied to obtain an approximation result for flat homomorphisms from algebras.