Extended degree functions and monomial modules

Abstract

The arithmetic degree, the smallest extended degree, and the homological degree are invariants that have been proposed as alternatives of the degree of a module if this module is not Cohen-Macaulay. We compare these degree functions and study their behavior when passing to the generic initial or the lexicographic submodule. This leads to various bounds and to counterexamples to a conjecture of Gunston and Vasconcelos, respectively. Particular attention is given to the class of sequentially Cohen-Macaulay modules. The results in this case lead to an algorithm that computes the smallest extended degree.

20 pages

References in corpus (3)

• What can be computed in algebraic geometry?
• Sequentially Cohen-Macaulay modules and local cohomology
• Ideals with maximal local cohomology modules

Cited by in corpus (3)

• On the structure of finitely generated modules and the unmixed degrees
• Finite Filtrations of Modules and Shellable Multicomplexes
• Algebraic shifting and exterior and symmetric algebra methods