Bigeneric initial ideals, diagonal subalgebras and bigraded Hilbert functions

DOI10.1016/S0022-4049(99)00100-0zbMath0995.13011OpenAlexW2031224077MaRDI QIDQ1577503

Emanuela De Negri, Kristina Crona, Annetta G. Aramova

Publication date: 11 January 2001

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0022-4049(99)00100-0

zbMATH Keywords

Castelnuovo-Mumford regularityinitial idealbigraded Hilbert functionsbilex idealdiagonal subalgebras

Mathematics Subject Classification ID

Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Graded rings (13A02)

Related Items (22)

Multigraded Castelnuovo-Mumford regularity via Klyachko filtrations ⋮ Minimal free resolutions and asymptotic behavior of multigraded regularity ⋮ The Simplest Minimal Free Resolutions in $${\mathbb {P}^1 \times \mathbb {P}^1}$$ ⋮ On linear resolution of powers of an ideal ⋮ Multigraded regularity: Coarsenings and resolutions ⋮ Radical generic initial ideals ⋮ Linear spaces, transversal polymatroids and ASL domains ⋮ Multigraded regularity, \(a^{*}\)-invariant and the minimal free resolution ⋮ On bigraded regularities of Rees algebra ⋮ Computing the resolution regularity of bi-homogeneous ideals ⋮ The regularity of points in multi-projective spaces. ⋮ The Hilbert function of bigraded algebras in \(k[\mathbb{P}^1 \times \mathbb{P}^1\)] ⋮ Betti numbers of strongly color-stable ideals and squarefree strongly color-stable ideals ⋮ Koszul property of diagonal subalgebras ⋮ Syzygies and singularities of tensor product surfaces of bidegree (2,1) ⋮ Uniform bounds on multigraded regularity ⋮ ON A CLASS OF MONOMIAL IDEALS ⋮ A numerical property of Hilbert functions and lex segment ideals ⋮ Subalgebras of bigraded Koszul algebras ⋮ Standard Bigraded Hilbert Functions ⋮ The border of the Hilbert function of a set of points in \(\mathbb P^{n_1}\times \cdots \times \mathbb P^{n_k}\) ⋮ Linear Resolutions of Powers and Products

Cites Work

• Minimal resolutions of some monomial ideals
• A theorem on refining division orders by the reverse lexicographic order
• Initial ideals, Veronese subrings, and rates of algebras
• Hilbert functions of graded algebras over Artinian rings
• Koszul cycles and Eliahou-Kervaire type resolutions
• Diagonal subalgebras of bigraded algebras and embeddings of blow-ups of projective spaces
• Upper bounds for the betti numbers of a given hilbert function
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