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 | Enthalten in: | ACTA MATHEMATICA VIETNAMICA | Band: | 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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