An Artinian ideal of in a 2-dimensional polynomial ring has many Hilbert-Burch matrices. We show that there is a canonical choice. As an application, we determine the dimension of certain affine Gr\"obner cells and their Betti strata recovering results of Ellingsrud and Stromme, Gottsche and Iarrobino.
Canonical Hilbert-Burch matrices for ideals in k[x,y]
CONCA, ALDO;VALLA, GIUSEPPE
2008-01-01
Abstract
An Artinian ideal of in a 2-dimensional polynomial ring has many Hilbert-Burch matrices. We show that there is a canonical choice. As an application, we determine the dimension of certain affine Gr\"obner cells and their Betti strata recovering results of Ellingsrud and Stromme, Gottsche and Iarrobino.
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