Comparing Castelnuovo-Mumford regularity and extended degree: the borderline cases

2003/11/28 by Uwe Nagel, Nagel, Uwe · 1 citation
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Polynomial and algebraic computation #math.AC #math.AG

paper · pdf · doi:10.48550/arxiv.math/0311534

arxiv created 2003/11/28 · arxiv updated 2009/12/01

Abstract

Castelnuovo-Mumford regularity and any extended degree function can be thought of as complexity measures for the structure of finitely generated graded modules. A recent result of Doering, Gunston, Vasconcelos shows that both can be compared in case of a graded algebra. We extend this result to modules and analyze when the estimate is in fact an equality. A complete classification is obtained if we choose as extended degree the homological or the smallest extended degree. The corresponding algebras are characterized in three ways: by relations among the algebra generators, by using generic initial ideals, and by their Hilbert series.

Cited by

• Algebraic invariants of the special fiber ring of ladder determinantal modules

Related

• Castelnuovo-Mumford regularity of Ext modules and homological degree
• Bounds for the Castelnuovo-Mumford regularity of modules
• Castelnuovo-Mumford regularity of the associated graded module in dimension one
• Linearly presented modules and bounds on the Castelnuovo-Mumford regularity of ideals
• Castelnuovo Mumford Regularity with respect to multigraded ideals