Hilbert-Kunz function of monomial ideals and binomial hypersurfaces.
Universally Koszul algebras defined by monomials
Algebre di Koszul
The goal of the talk is to introduce and discuss the notion Koszul algebra in the commutative setting along with the associated notions of G-quadraticity and Koszul filtration. We present some results that appear in the papers [C, CTV, CRV] joint with M.E.Rossi, N.V.Trung and G.Valla. These results concern Koszul and G-quadratic properties of algebras associated with points, curves, cubics and spaces of quadrics of low codimension.
The dimension of certain catalecticant varieties.
Castelnuovo-Mumford regularity of products of ideals.
The Castelnuovo-Mumford regularity reg(M) is one of the most important invariants of a finitely generated graded module M over a polynomial ring R. For instance, it measures the amount of computational resources that working with M requires. In general one knows that the regularity of a module can be doubly exponential in the degrees of the minimal generators and in the number of the variables. On the other hand, in many situations one has or one conjectures a much better behavior. One may ask,...
Regular Sequences of Symmetric Polynomials
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