A note on minimal resolutions of vector–spread Borel ideals

Marilena Crupi; Antonino Ficarra

doi:10.2478/auom-2023-0020

.blurhash-client-img { display: none !important; }

A note on minimal resolutions of vector–spread Borel ideals

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 31 (2023): Issue 2 (March 2023)

By: Marilena Crupi and Antonino Ficarra

Open Access

|Mar 2023

Abstract

We consider vector–spread Borel ideals. We show that these ideals have linear quotients and thereby we determine the graded Betti numbers and the bigraded Poincaré series. A characterization of the extremal Betti numbers of such a class of ideals is given. Finally, we classify all Cohen–Macaulay vector–spread Borel ideals.

References

L. Amata, M. Crupi, Extremal Betti numbers of t–spread strongly stable ideals, Mathematics 7(695) (2019).
Search in Google Scholar Back to article
L. Amata, M. Crupi, A. Ficarra, Upper bounds for extremal Betti numbers of t–spread strongly stable ideals, Bull. Math. Soc. Sci. Math. Roumanie 65 (113), No. 1 (2022), 13–34.
Search in Google Scholar Back to article
L. Amata, A. Ficarra, M. Crupi, A numerical characterization of the extremal Betti numbers of t-spread strongly stable ideals, J. Algebr. Comb. 55, 891–918 (2022)
Search in Google Scholar Back to article
L. Amata, M. Crupi, A. Ficarra, Projective dimension and Castelnuovo– Mumford regularity of t–spread ideals, Internat. J. Algebra Comput 32 No. 4 (2022), 837–858
Search in Google Scholar Back to article
C. Andrei, V. Ene, B. Lajmiri, Powers of t–spread principal Borel ideals, Arch. Math. 112(6) (2019), 587–597.
Search in Google Scholar Back to article
A. Aramova, J. Herzog, T. Hibi, Shifting Operations and Graded Betti Numbers, J. Algebr. Comb. 12 (2000), 207–222.
Search in Google Scholar Back to article
D. Bayer, H. Charalambous, S. Popescu, Extremal Betti numbers and applications to monomial ideals, J. Algebra 221 (1999), 497–512.
Search in Google Scholar Back to article
W. Bruns, J. Herzog, Cohen-Macaulay rings, Revised Ed., Cambridge University Press, 1998.
Search in Google Scholar Back to article
M. Crupi, Extremal Betti numbers of graded modules, J. Pure Appl. Algebra 220 (2016), 2277–2288.
Search in Google Scholar Back to article
M. Crupi, C. Ferrò, Squarefree monomial modules and extremal Betti numbers, Algebra Colloq. 23 (2016), 519–530.
Search in Google Scholar Back to article
M. Crupi, A. Ficarra, Classification of Cohen–Macaulay t–spread lexsegment ideals via simplicial complexes, Illinois J. Math., Advance Publication 1–30, 2022. DOI: 10.1215/00192082-10201831.
Open DOI Search in Google Scholar Back to article
R. Dinu, J. Herzog, A. A. Qureshi, Restricted classes of veronese type ideals and algebras, Internat. J. Algebra Comput. 31(01) (2021), 173–197.
Search in Google Scholar Back to article
V. Ene, J. Herzog, A. A. Qureshi, t–spread strongly stable monomial ideals, Comm. Algebra 47 (12) (2019), 5303–5316.
Search in Google Scholar Back to article
D. R. Grayson, M. E. Stillman, Macaulay2, a software system for research in algebraic geometry. Available at http://www.math.uiuc.edu/Macaulay2.
Search in Google Scholar Back to article
A. Ficarra, Vector–spread monomial ideals and Eliahou–Kervaire type resolution, J. Algebra 615 (2023), 170–204.
Search in Google Scholar Back to article
J. Herzog, T. Hibi, Monomial ideals, Graduate texts in Mathematics 260, Springer–Verlag, 2011.
Search in Google Scholar Back to article
J. Herzog, Y. Takayama, Resolutions by mapping cones, in: The Roos Festschrift volume Nr.2(2), Homology, Homotopy and Applications 4 (2002), 277–294.
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/auom-2023-0020 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784

Journal RSS Feed

Language: English

Page range: 71 - 84

Submitted on: Jun 21, 2022

Accepted on: Nov 21, 2022

Published on: Mar 27, 2023

Published by: Ovidius University of Constanta

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

monomial ideals,

vector–spread Borel ideals,

Cohen–Macaulay ideals,

extremal Betti numbers

Related subjects:

Mathematics,

General mathematics

© 2023 Marilena Crupi, Antonino Ficarra, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 31 (2023): Issue 2 (March 2023)