9 citations · 56 across the 26 of their papers we have counts for
5 papers · 1 filter
Generic circuits sets and general initial ideals with respect to weights
Giulio Caviglia, Enrico Sbarra
We study the set of circuits of a homogeneous ideal and that of its truncations, and introduce the notion of generic circuits set. We show how this is a well-defined invariant that…
Componentwise regularity (I)
Giulio Caviglia, Matteo Varbaro
We define the notion of componentwise regularity and study some of its basic properties. We prove an analogue, when working with weight orders, of Buchberger's criterion to compute…
Distractions of Shakin rings
Giulio Caviglia, Enrico Sbarra
We study, by means of embeddings of Hilbert functions, a class of rings which we call Shakin rings, i.e. quotients K[X_1,...,X_n]/a of a polynomial ring over a field K by ideals a=…
On Hilbert functions of general intersections of ideals
Giulio Caviglia, Satoshi Murai
Let I and J be homogeneous ideals in a standard graded polynomial ring. We study upper bounds of the Hilbert function of the intersection of I and g(J), where g is a general change…
Zero-generic initial ideals
Giulio Caviglia, Enrico Sbarra
Given a homogeneous ideal I of a polynomial ring A=K[X_1,...,X_n] and a monomial order, we construct a new monomial ideal of A associated with I. We call it the zero-generic initia…