Virtual resolutions of monomial ideals on toric varieties
HTML articles powered by AMS MathViewer
Abstract:
We use cellular resolutions of monomial ideals to prove an analog of Hilbert’s syzygy theorem for virtual resolutions of monomial ideals on smooth toric varieties.References
- Dave Bayer, Irena Peeva, and Bernd Sturmfels, Monomial resolutions, Math. Res. Lett. 5 (1998), no. 1-2, 31–46. MR 1618363, DOI 10.4310/MRL.1998.v5.n1.a3
- Dave Bayer and Bernd Sturmfels, Cellular resolutions of monomial modules, J. Reine Angew. Math. 502 (1998), 123–140. MR 1647559, DOI 10.1515/crll.1998.083
- Christine Berkesch, The rank of a hypergeometric system, Compos. Math. 147 (2011), no. 1, 284–318. MR 2771133, DOI 10.1112/S0010437X10004811
- Christine Berkesch, Daniel Erman, and Gregory G. Smith, Virtual resolutions for a product of projective spaces, Algebr. Geom. 7 (2020), no. 4, 460–481. MR 4156411, DOI 10.14231/ag-2020-013
- Anna Maria Bigatti, Upper bounds for the Betti numbers of a given Hilbert function, Comm. Algebra 21 (1993), no. 7, 2317–2334. MR 1218500, DOI 10.1080/00927879308824679
- Allen Hatcher, Algebraic topology, Cambridge University Press, Cambridge, 2002. MR 1867354
- Heather Ann Hulett, Maximum Betti numbers for a given Hilbert function, ProQuest LLC, Ann Arbor, MI, 1993. Thesis (Ph.D.)–University of Illinois at Urbana-Champaign. MR 2690379
- Sarah Mayes-Tang, Stabilization of Boij-Söderberg decompositions of ideal powers, J. Pure Appl. Algebra 223 (2019), no. 2, 571–579. MR 3850557, DOI 10.1016/j.jpaa.2018.04.007
- Ezra Miller, Topological Cohen-Macaulay criteria for monomial ideals, Combinatorial aspects of commutative algebra, Contemp. Math., vol. 502, Amer. Math. Soc., Providence, RI, 2009, pp. 137–155. MR 2583278, DOI 10.1090/conm/502/09861
- Ezra Miller and Bernd Sturmfels, Combinatorial commutative algebra, Graduate Texts in Mathematics, vol. 227, Springer-Verlag, New York, 2005. MR 2110098
- Keith Pardue, Deformation classes of graded modules and maximal Betti numbers, Illinois J. Math. 40 (1996), no. 4, 564–585. MR 1415019
- Gwyneth Whieldon, Stabilization of Betti tables, J. Commut. Algebra 6 (2014), no. 1, 113–126. MR 3215565, DOI 10.1216/JCA-2014-6-1-113
Additional Information
- Jay Yang
- Affiliation: School of Mathematics, University of Minnesota, 206 Church Street SE, Minneapolis, Minnesota 55455
- MR Author ID: 1303201
- ORCID: 0000-0001-8366-423X
- Email: jkyang@umn.edu
- Received by editor(s): September 13, 2019
- Received by editor(s) in revised form: July 29, 2020
- Published electronically: February 16, 2021
- Additional Notes: The author was supported by NSF DMS-1502553 and DMS-1745638.
- Communicated by: Claudia Polini
- © Copyright 2021 by the author under Creative Commons Attribution 3.0 License (CC BY 3.0)
- Journal: Proc. Amer. Math. Soc. Ser. B 8 (2021), 100-111
- MSC (2020): Primary 13D02; Secondary 05E40, 14M25
- DOI: https://doi.org/10.1090/bproc/72
- MathSciNet review: 4215648