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Families of reduced zero-dimensional schemes.

Juan C. Migliore (2006)

Collectanea Mathematica

A great deal of recent activity has centered on the question of whether, for a given Hilbert function, there can fail to be a unique minimum set of graded Betti numbers, and this is closely related to the question of whether the associated Hilbert scheme is irreducible or not. We give a broad class of Hilbert functions for which we show that there is no minimum, and hence that the associated Hilbert sheme is reducible. Furthermore, we show that the Weak Lefschetz Property holds for the general element...

(Generalized) filter properties of the amalgamated algebra

Yusof Azimi (2022)

Archivum Mathematicum

Let R and S be commutative rings with unity, f : R → S a ring homomorphism and J an ideal of S . Then the subring R ⋈ f J : = { ( a , f ( a ) + j ) ∣ a ∈ R and j ∈ J } of R × S is called the amalgamation of R with S along J with respect to f . In this paper, we determine when R ⋈ f J is a (generalized) filter ring.

Gorenstein liaison of some curves in P4.

Joshua Lesperance (2001)

Collectanea Mathematica

Despite the recent advances made in Gorenstein liaison, there are still many open questions for the theory in codimension ≥ 3. In particular we consider the following question: given two curves in Pn with isomorphic deficiency modules (up to shift), can they be evenly Gorenstein linked? The answer for this is yes for curves in P3, due to Rao, but for higher codimension the answer is not known. This paper will look at large classes of curves in P4 with isomorphic deficiency modules and show that...

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