Marco D'Anna: Numerical duplication and its associated graded ring

I will present a ring construction obtained considering quadratic quotients of the Rees algebra of a commutative ring with respect to an ideal, and its corresponding semigroup construction, called numerical duplication. In particular, I will present some properties of the numerical semigroup ring associated to a numerical duplication and of its associated graded ring (i.e. the tangent cone at the origin of the corresponding monomial curve). We will characterize numerically the Cohen–Macaulay, Gorenstein and complete intersection properties for these associated graded rings and, as a by-product, we will get conditions for the canonical ideal of the tangent cone of a monomial curve to be of the expected form.

This is a joint work with Raheleh Jafari and Francesco Strazzanti.