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LYUBEZNIK NUMBERS OF LOCAL RINGS AND LINEAR STRANDS OF GRADED IDEALS

  • JOSEP ÀLVAREZ MONTANER (a1) and KOHJI YANAGAWA (a2)

Abstract

In this work, we introduce a new set of invariants associated to the linear strands of a minimal free resolution of a $\mathbb{Z}$ -graded ideal $I\subseteq R=\Bbbk [x_{1},\ldots ,x_{n}]$ . We also prove that these invariants satisfy some properties analogous to those of Lyubeznik numbers of local rings. In particular, they satisfy a consecutiveness property that we prove first for the Lyubeznik table. For the case of squarefree monomial ideals, we get more insight into the relation between Lyubeznik numbers and the linear strands of their associated Alexander dual ideals. Finally, we prove that Lyubeznik numbers of Stanley–Reisner rings are not only an algebraic invariant but also a topological invariant, meaning that they depend on the homeomorphic class of the geometric realization of the associated simplicial complex and the characteristic of the base field.

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The first author was partially supported by Generalitat de Catalunya 2014SGR-634 project and Spanish Ministerio de Economía y Competitividad MTM2015-69135-P. The second author was partially supported by JSPS KAKENHI 25400057

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References

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