Antonino Ficarra: Homological shifts of polymatroidal ideals, 463-472

Abstract:

We study the homological shifts of polymatroidal ideals. In our main theorem we prove that the first homological shift ideal of any polymatroidal ideal is again polymatroidal, supporting a conjecture of Bandari, Bayati and Herzog that predicts that all homological shift ideals of a polymatroidal ideal are polymatroidal. As a nice consequence, we recover a result of Bayati which proves this conjecture in the squarefree case.

Key Words: Monomial ideals, minimal resolution, multigraded shifts, polymatroidal ideals.

2020 Mathematics Subject Classification: 05B35, 05E40, 13B25, 13D02, 68W30.

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