Exterior algebra methods for the minimal resolution conjecture.

DOI10.1215/S0012-9074-02-11226-5zbMath1035.13008arXivmath/0011236WikidataQ123269085 ScholiaQ123269085MaRDI QIDQ1847916

David Eisenbud, Sorin Popescu, Charles Walter, Frank-Olaf Schreyer

Publication date: 27 October 2002

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0011236

zbMATH Keywords

exterior algebragraded Betti numbersminimal resolution conjectureBernstein-Gelfand-Gelfand correspondence

Mathematics Subject Classification ID

Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) (14M05) Projective and free modules and ideals in commutative rings (13C10) Syzygies, resolutions, complexes and commutative rings (13D02) Exterior algebra, Grassmann algebras (15A75)

Related Items

The minimal resolution conjecture on a general quartic surface in \(\mathbb{P}^3\), Minimal resolutions, Chow forms and Ulrich bundles on \(K3\) surfaces, Minimal free resolution for points on surfaces, Minimal free resolutions of general points lying on cubic surfaces in \(\mathbb P^3\), Sheaf cohomology and free resolutions over exterior algebras, Divisors on and the minimal resolution conjecture for points on canonical curves, Periodic resolutions over exterior algebras.

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Codimension and multiplicity
• Koszul cohomology and the geometry of projective varieties. Appendix: The nonvanishing of certain Koszul cohomology groups (by Mark Green and Robert Lazarsfeld)
• The Eisenbud-Koh-Stillman conjecture on linear syzygies
• Gale duality and free resolutions of ideals of points
• The minimal resolution conjecture
• Maximal rank for \(T_{\mathbb{P}^n}\)
• The projective geometry of the Gale transform.
• Generating modules efficiently: Theorems from algebraic K-theory
• The minimal free resolution of the homogeneous ideal of \(s\) general points in \(\mathbb{P}^ 4\)
• Artin level modules
• Betti numbers of points in projective space
• On the Canonical Module of A 0-Dimensional Scheme
• Sheaf cohomology and free resolutions over exterior algebras
• Linear Sections of Determinantal Varieties
• The minimal resolution of the ideal of a general arrangement of a big number of points in \(\mathbb{P}^ n\)