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The homological degree of a module |
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| Authors: | Wolmer V. Vasconcelos |
| Affiliation: | Department of Mathematics - Hill Center, Rutgers University, 110 Frelinghuysen RD, Piscataway, New Jersey 08854-8019 |
| Abstract: | A homological degree of a graded module  is an extension of the usual notion of multiplicity tailored to provide a numerical signature for the module even when  is not Cohen-Macaulay. We construct a degree,  , that behaves well under hyperplane sections and the modding out of elements of finite support. When carried out in a local algebra this degree gives a simulacrum of complexity à la Castelnuovo-Mumford's regularity. Several applications for estimating reduction numbers of ideals and predictions on the outcome of Noether normalizations are given. |
| Keywords: | Arithmetic degree Castelnuovo-Mumford regularity geometric degree Gorenstein ring homological degree reduction number |
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