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Castelnuovo-Mumford regularity of products of ideals.

Aldo Conca, Jürgen Herzog (2003)

Collectanea Mathematica

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,...

Castelnuovo's index of regularity and reduction numbers

Peter Schenzel (1990)

Banach Center Publications

Characterizations of some rings with $𝒞$ -projective, $𝒞$ -(FP)-injective and $𝒞$ -flat modules

Xiao Guang Yan, Xiao Sheng Zhu (2011)

Czechoslovak Mathematical Journal

Let $R$ be a commutative ring and $𝒞$ a semidualizing $R$ -module. We investigate the relations between $𝒞$ -flat modules and $𝒞$ -FP-injective modules and use these modules and their character modules to characterize some rings, including artinian, noetherian and coherent rings.

Classifying Hilbert functions of fat point subschemes in P^2.

Anthony Vito Geramita, Brian Harbourne, Juan Migliore (2009)

Collectanea Mathematica

Cohen-Macaulay modifications of the vertex cover ideal of a graph

Safyan Ahmad, Shamsa Kanwal, Talat Firdous (2018)

Czechoslovak Mathematical Journal

We study when the modifications of the Cohen-Macaulay vertex cover ideal of a graph are Cohen-Macaulay.

Combinatoric of syzygies for semigroup algebras.

Emilio Briales, Pilar Pisón, Antonio Campillo, Carlos Marijuán (1998)

Collectanea Mathematica

We describe how the graded minimal resolution of certain semigroup algebras is related to the combinatorics of some simplicial complexes. We obtain characterizations of the Cohen-Macaulay and Gorenstein conditions. The Cohen-Macaulay type is computed from combinatorics. As an application, we compute explicitly the graded minimal resolution of monomial both affine and simplicial projective surfaces.

Completeness conditions in certain Weyl complexes, combinatorics and parsimony.

Sano, Mari (2005)

Boletín de la Asociación Matemática Venezolana

Cremona transformations and syzygies.

F.-O. Schreyer, K. Hulek, S. Katz (1992)

Mathematische Zeitschrift

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