Computing Hilbert Functions Using The Syzygy And Lcm Lattice Methods
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Computing Hilbert Functions Using the Syzygy and LCM-lattice Methods
Author | : Maria Barouti |
Publisher | : |
Total Pages | : 88 |
Release | : 2011 |
Genre | : Algebra, Homological |
ISBN | : |
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"The Hilbert function for any graded module over a field k is defined by the dimension of all of the summands M_b, where b indicates the graded component being considered. One standard approach to computing the Hilbert function is to come up with a free-resolution for the graded module M and another is via a Hilbert power series which serves as a generating function. Using combinatorics and homological algebra we develop three alternative ways to generate the values of a Hilbert function when the graded module is a quotient ring over a field. Two of these approaches (which we've called the lcm-Lattice method and the Syzygy method) are conceptually combinatorial and work for any polynomial quotient ring over a field. The third approach, which we call the Hilbert function table method, also uses syzygies but the approach is better described in terms of homological algebra."--Abstract.
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