Some algebras with the weak Lefschetz property

David Cook; Uwe Nagel

doi:10.1007/978-3-319-61943-9_4

Some algebras with the weak Lefschetz property

David Cook, Uwe Nagel

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Using a connection to lozenge tilings of triangular regions, we establish an easily checkable criterion that guarantees the weak Lefschetz property of a quotient by a monomial ideal in three variables. It is also shown that each such ideal also has a semistable syzygy bundle.

Original language	English
Pages (from-to)	69-80
Number of pages	12
Journal	Springer INdAM Series
Volume	20
DOIs	https://doi.org/10.1007/978-3-319-61943-9_4
State	Published - 2017

Bibliographical note

Funding Information:
Fig. 6 The region corresponding to d1 D d2 D d3 D 12 and d4 D ∆∆∆ D d8 D 11 in Example 3 Acknowledgements The second author was partially supported by the National Security Agency under Grant Number H98230-12-1-0247 and by the Simons Foundation under grants #208869 and #317096. The authors are grateful to the referee for comments that helped to improve the exposition.

Publisher Copyright:
© 2017, Springer International Publishing AG.

Keywords

Determinants
Lozenge tiling
Monomial ideal
Perfect matching
Semistable syzygy bundle
Weak Lefschetz property

ASJC Scopus subject areas

Mathematics (all)

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10.1007/978-3-319-61943-9_4

Cite this

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N2 - Using a connection to lozenge tilings of triangular regions, we establish an easily checkable criterion that guarantees the weak Lefschetz property of a quotient by a monomial ideal in three variables. It is also shown that each such ideal also has a semistable syzygy bundle.

AB - Using a connection to lozenge tilings of triangular regions, we establish an easily checkable criterion that guarantees the weak Lefschetz property of a quotient by a monomial ideal in three variables. It is also shown that each such ideal also has a semistable syzygy bundle.

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KW - Perfect matching

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ER -

Some algebras with the weak Lefschetz property

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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