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.
|Number of pages||12|
|Journal||Springer INdAM Series|
|State||Published - 2017|
Bibliographical noteFunding 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.
© 2017, Springer International Publishing AG.
- Lozenge tiling
- Monomial ideal
- Perfect matching
- Semistable syzygy bundle
- Weak Lefschetz property
ASJC Scopus subject areas
- Mathematics (all)