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On the jacobian module associated to a graph |
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| Authors: | Aron Simis |
| Institution: | Instituto de Matemática, Universidade Federal da Bahia, Av. Ademar de Barros, s/n, 40170-210 Salvador, BA, Brazil |
| Abstract: | We consider the jacobian module of a set ![$\bold{f}:=\{f_1,\ldots,f_m\} \in R:=kX_1,\ldots,X_n]$](http://www.ams.org/proc/1998-126-04/S0002-9939-98-04180-X/gif-abstract/img1.gif) of squarefree monomials of degree  corresponding to the edges of a connected bipartite graph  . We show that for such a graph  the number of its primitive cycles (i.e., cycles whose chords are not edges of  ) is the second Betti number in a minimal resolution of the corresponding jacobian module. A byproduct is a graph theoretic criterion for the subalgebra ![$kG]:=k\bold{f}]$](http://www.ams.org/proc/1998-126-04/S0002-9939-98-04180-X/gif-abstract/img6.gif) to be a complete intersection. |
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