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Regularity and multiplicity of toric rings of three-dimensional Ferrers diagrams
We investigate the Castelnuovo--Mumford regularity and the multiplicity of
the toric ring associated to a three-dimensional Ferrers diagram. In
particular, in the rectangular case, we are able to provide direct formulas for
these two important invariants. Then, we compare these invariants for an
accompanied pair of Ferrers diagrams under some mild conditions, and bound the
Castelnuovo--Mumford regularity for more general cases.Comment: 22 pages, 2 figures and comments are welcom
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