Subcomplexes of Certain Free Resolutions

Banks, Maya; Sobieska, Aleksandra

doi:10.48550/arxiv.2112.15137

Cited by 1 publication

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“…In Appendix B, we explicitly construct this isomorphism. Recently, there has been considerable interest in subcomplexes of free resolutions, particularly fundamental complexes such as the Eagon-Northcott complex [4]. The minimal free resolution F 1,Π contains minimal free resolutions of the toppling ideals of each its connected partition graphs as subcomplexes, we refer to Subsection 3.4 and Appendix B for more details.…”

Section: Other Results and Applicationsmentioning

confidence: 99%

Rational Normal Curves, Chip Firing and Betti Strata

Karki¹,

Manjunath²

2023

Preprint

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We study Betti strata of rational normal curves via a connection to the chip firing game. Our main results are: i. a comparison theorem that states that any Cohen-Macaulay initial monomial ideal of the rational normal curve (of a given degree and embedded in the standard form) shares its graded Betti table with the corresponding rational normal curve, ii. a connectivity theorem that explicitly constructs a family of minimal free resolutions that interpolates between the minimal free resolution of the rational normal curve and a Cohen-Macaulay initial monomial ideal thereof. The key technique, introduced in this article, is to interpret the defining ideal of the rational normal curve as an ideal associated to a generalisation of a cycle graph called a parcycle. This association allows us to study rational normal curves via combinatorial methods. Other results include a combinatorial minimal free resolution for the rational normal curve and minimal cellular resolutions for all its Cohen-Macaulay initial monomial ideals.

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Section: Other Results and Applicationsmentioning

confidence: 99%