140
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

Minimal Castelnuovo–Mumford Regularity for a Given Hilbert Polynomial

, , &

References

  • [Ballico et al. 11] E. Ballico, C. Bertone, and M. Roggero. “The Locus of Points of the Hilbert Scheme with Bounded Regularity.” In Press on Comm. in Algebra. Available at http://arxiv.org/abs/1111.2007arXiv:1111.2007, 2011. DOI: 10.1080/00927872.2014.907905
  • [Bayer and Mumford 93] D. Bayer, and D. Mumford. “What Can Be Computed in Algebraic Geometry?” In Computational Algebraic Geometry and Commutative Algebra (Cortona, 1991), Sympos. Math., XXXIV, pp. 1–48. Cambridge: Cambridge Univ. Press, 1993.
  • [Bayer and Stillman 87] D. Bayer, and M. Stillman. “A Criterion for Detecting m-Regularity.” Invent Math. 87: 1 (1987), 1–11. DOI: 10.1007/BF01389151.
  • [Brodmann 10] M. P. Brodmann. Around Castelnuovo–Mumford Regularity. Available online (http://www.math. uzh.ch/fileadmin/user/brodmann/publikation/AROUND.REGU LARITY.pdf), 2010.
  • [Caviglia and Sbarra 14] G. Caviglia, and E. Sbarra. Zero-generic Initial Ideals. Available online (http://arxiv.org/abs/1303.5373), 2014.
  • [Cioffi and Di Gennaro 11] F. Cioffi, and R. Di Gennaro. “Liaison and Cohen-Macaulayness Conditions.” Collect Math. 62: 2 (2011), 173–186. DOI: 10.1007/s13348-010-0010-z.
  • [Cioffi et al. 09] F. Cioffi, M. G. Marinari, and L. Ramella. “Regularity Bounds by Minimal Generators and Hilbert Function.” Collect Math. 60: 1 (2009), 89–100. DOI: 10.1007/BF03191218.
  • [Cioffi et al. 11] F. Cioffi, P. Lella, M. G. Marinari, and M. Roggero. “Segments and Hilbert Schemes of Points.” Discrete Math. 311: 20 (2011), 2238–2252. DOI: 10.1016/j.disc.2011.07.011.
  • [Geramita et al. 83] A. V. Geramita, P. Maroscia, and L. G. Roberts. “The Hilbert Function of a Reduced k-Algebra.” J. London Math. Soc. (2). 28: 3 (1983), 443–452. DOI: 10.1112/jlms/s2-28.3.443.
  • [Gotzmann 78] G. Gotzmann. “Eine Bedingung Für die Flachheit und das Hilbertpolynom eines graduierten Ringes.” Math. Z. 158: 1 (1978), 61–70.
  • [Green 10] M. L. Green. “Generic Initial Ideals.” In Six Lectures on Commutative Algebra, Mod. Birkhäuser Class, pp. 119–186. Basel: Birkhäuser Verlag, 2010.
  • [Hartshorne 66] R. Hartshorne. “Connectedness of the Hilbert Scheme.” Inst. Hautes Études Sci. Publ. Math. 29 (1966), 5–48.
  • [Lella 12]P. Lella. “An Efficient Implementation of the Algorithm Computing the Borel-fixed Points of a Hilbert Scheme.” In ISSAC 2012-Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation, pp. 242–248. New York: ACM, 2012.
  • [Macaulay 26] F. S. Macaulay. “Some Properties of Enumeration in the Theory of Modular Systems.” Proc. London Math. Soc. 26 (1926), 531–555.
  • [Mall 97] D. Mall. “Betti Numbers, Castelnuovo–Mumford Regularity, and Generalisations of Macaulay’s Theorem.” Commun. Algebra. 25: 12 (1997), 3841–3852, DOI: 10.1080/00927879708826090.
  • [Mall 00] D. Mall. “Connectedness of Hilbert Function Strata and Other Connectedness Results.” J. Pure Appl. Algebra. 150: 2 (2000), 175–205. DOI: 10.1016/S0022-4049(99)00068-7.
  • [Marinari and Ramella 99] M. G. Marinari, and L. Ramella. “Some Properties of Borel Ideals.” J. Pure Appl. Algebra. 139: 1–3 (1999), 183–200. DOI: 10.1016/S0022-4049(99)00011-0. (Effective Methods in Algebraic Geometry (Saint-Malo, 1998)).
  • [Marinari and Ramella 06] M. G. Marinari, and L. Ramella. “Borel Ideals in Three Variables.” Beiträge Algebra Geom. 47: 1 (2006), 195–209.
  • [Robbiano 90] L. Robbiano. “Introduction to the Theory of Hilbert Functions.” In The Curves Seminar at Queen’s, Vol. VII, (Kingston, ON, 1990), Queen’s Papers in Pure and Appl. Math., vol 85, pp. Exp. No. B, 26. Kingston, ON: Queen’s Univ., 1990.
  • [Roberts 82] L. G. Roberts. “Hilbert Polynomials and Minimum Hilbert Functions.” In The Curves Seminar at Queens, Vol. II (Kingston, Ont., 1981/1982), Queen’s Papers in Pure and Appl. Math., vol 61, pp. Exp. No. F, 21. Kingston, ON: Queen’s Univ., 1982.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.