The Chern and Euler Coefficients of Modules

Details The Chern and Euler Coefficients of Modules The Chern and Euler Coefficients of Modules

2011-09-26

arxiv.org/abs/1109.5628v1

Mathematics

Commutative Algebra

Scientific paper

The set of the first Hilbert coefficients of parameter ideals relative to a module--its Chern coefficients--over a local Noetherian ring codes for considerable information about its structure--noteworthy properties such as that of Cohen-Macaulayness, Buchsbaumness, and of having finitely generated local cohomology. The authors have previously studied the ring case. By developing a robust setting to treat these coefficients for unmixed rings and modules, the case of modules is analyzed in a more transparent manner. Another series of integers arise from partial Euler characteristics and are shown to carry similar properties of the module. The technology of homological degree theory is also introduced in order to derive bounds for these two sets of numbers.

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