Regularity and multiplicity of toric rings of three-dimensional Ferrers diagrams

Abstract

We investigate the Castelnuovo-Mumford regularity and the multiplicity of the toric ring associated with a three-dimensional Ferrers diagram. In particular, in the rectangular case, we provide direct formulas for these two important invariants. Then, we compare these invariants for an accompanying pair of Ferrers diagrams under some mild conditions and bound the Castelnuovo-Mumford regularity for more general cases.

Revised following the reviewer's suggestions. 27 pages and 6 figures. Comments are welcome

References in corpus (3)

• The Maximum Likelihood Degree of Toric Varieties
• Square-free Groebner degenerations
• Toric Varieties and Codes, Error-correcting Codes, Quantum Codes, Secret Sharing and Decoding

Cited by in corpus (1)

• On the conjecture of Vasconcelos for Artinian almost complete intersection monomial ideals