Nagata's Criterion and Openness of Loci for Gorenstein and Complete Intersection.
Nicht-ausgeartete reguläre Überlagerungen.
Normal and tangential flatness.
Note on Asymptotic Prime Divisors and Symbolic Powers of Primary Ideals.
Notes on an extension of Krull's principal ideal theorem
Notes on the multiplicity conjecture.
New cases of the multiplicity conjecture are considered.
Numerical characters of graded algebras
This is the summary of the plenary talk I gave in Milan at the XVII Meeting of the Unione Matematica Italiana. We focus on some relevant numerical characters of the standard graded algebras and, in some case, we explain their geometric meaning.
Numerical invariants of liasion classes.
Numerical semigroups of maximal and almost maximal length.
Numerical semigroups with a monotonic Apéry set
We study numerical semigroups with the property that if is the multiplicity of and is the least element of congruent with modulo , then . The set of numerical semigroups with this property and fixed multiplicity is bijective with an affine semigroup and consequently it can be described by a finite set of parameters. Invariants like the gender, type, embedding dimension and Frobenius number are computed for several families of this kind of numerical semigroups.