Graded Betti Numbers of Balanced Simplicial Complexes

Autor(en): Juhnke-Kubitzke, Martina 
Venturello, Lorenzo
Stichwörter: Balanced; Graded Betti numbers; IDEALS; Lex (plus powers) ideals; LOWER-BOUND THEOREMS; Mathematics; RESOLUTIONS; Simplicial complex; Stanley-Reisner ring
Erscheinungsdatum: 2021
Herausgeber: SPRINGER SINGAPORE PTE LTD
Journal: ACTA MATHEMATICA VIETNAMICA
Volumen: 46
Ausgabe: 4
Startseite: 839
Seitenende: 871
Zusammenfassung: 
We prove upper bounds for the graded Betti numbers of Stanley-Reisner rings of balanced simplicial complexes. Along the way we show bounds for Cohen-Macaulay graded rings S/I, where S is a polynomial ring and I subset of S is a homogeneous ideal containing a certain number of generators in degree 2, including the squares of the variables. Using similar techniques we provide upper bounds for the number of linear syzygies for Stanley-Reisner rings of balanced normal pseudomanifolds. Moreover, we compute explicitly the graded Betti numbers of cross-polytopal stacked spheres, and show that they only depend on the dimension and the number of vertices, rather than also the combinatorial type.
ISSN: 02514184
DOI: 10.1007/s40306-021-00449-8

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