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On the Regularity and Defect Sequence of Monomial and Binomial Ideals
When S is a polynomial ring or more generally a standard graded algebra over a field K , with homogeneous maximal ideal m, it is known that for an...
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Powers of t-spread principal Borel ideals
We prove that t -spread principal Borel ideals are sequentially Cohen–Macaulay and study their powers. We show that these ideals possess the strong...
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Cohen-Macaulay modifications of the vertex cover ideal of a graph
We study when the modifications of the Cohen-Macaulay vertex cover ideal of a graph are Cohen-Macaulay.
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The Birational Geometry of Moduli Spaces
The purpose of these lecture notes is to introduce the basics of the birational geometry of moduli spaces to students who have taken an introductory...
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A Construction of Totally Reflexive Modules
We construct infinite families of pairwise non-isomorphic indecomposable totally reflexive modules of high multiplicity. Under suitable conditions on...
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On the Stanley–Reisner ideal of an expanded simplicial complex
Let Δ be a simplicial complex. We study the expansions of Δ mainly to see how the algebraic and combinatorial properties of Δ and its expansions are...
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Extension Closedness of Syzygies and Local Gorensteinness of Commutative Rings
We refine a well-known theorem of Auslander and Reiten about the extension closedness of n th syzygies over noether algebras. Applying it, we obtain...
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Krull dimension for differential graded algebras
We introduce a naive notion of a system of parameters for a homologically finite complex over a commutative noetherian local ring and compare it to...
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Local Rings of Embedding Codepth 3. Examples
A complete local ring of embedding codepth 3 has a minimal free resolution of length 3 over a regular local ring. Such resolutions carry a...
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The equations of almost complete intersections
In this paper we inject four Hilbert functions in the determination of the defining equations of the Rees algebra of almost complete intersections of...
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A note on the weak Lefschetz property of monomial complete intersections in positive characteristic
Let K be an algebraically closed field of characteristic p > 0. We apply a theorem of Han to give an explicit description for the weak Lefschetz...
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Gaeta’s Work on Liaison Theory: An Appreciation
This short note is a survey of Gaeta’s results on Liaison theory.