For initial ideals of determinantal ideals with respect to diagonal monomial orders, the author proves SLP for maximal minors and WLP failure for non-maximal minors when mn is large enough.
Determinants, Gr¨ obner Bases and Cohomology
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On the weak and strong Lefschetz properties for initial ideals of determinantal ideals with respect to diagonal monomial orders
For initial ideals of determinantal ideals with respect to diagonal monomial orders, the author proves SLP for maximal minors and WLP failure for non-maximal minors when mn is large enough.