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arXiv · 1708.07255

The combinatorial calculation of algebraic invariants of a monomial ideal

Luis A. Dupont·Daniel G. Mendoza·Miriam Rodríguez
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Abstract

We introduce the combinatorial Lyubeznik resolution of monomial ideals. We prove that this resolution is isomorphic to the usual Lyubezbnik resolution. As an application, we give a combinatorial method to determine if an ideal is a Lyubeznik ideal. Furthermore, the minimality of the Lyubeznik resolution is characterized and we classify all the Lyubeznik symbols using combinatorial criteria. We get a combinatorial expression for the projective dimension, the length of Lyubeznik, and the arithmetical rank of a monomial ideal. We define the Lyubeznik totally ideals as those ideals that yield a minimal free resolution under any total order. Finally, we present that for a family of graphics, that their edge ideals are Lyubeznik totally ideals.

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Luis A. Dupont, Daniel G. Mendoza, Miriam Rodríguez. 2017-08-24. The combinatorial calculation of algebraic invariants of a monomial ideal. https://arxiv.org/abs/1708.07255

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