On the Castelnuovo-Mumford regularity index of the coordinate ring of a set of n + 3 non-degenerate fat points in projective space Pn
PDF (Vietnamese)

Keywords

Tập điểm béo; Chỉ số chính quy; Hàm Hilbert;Vành tọa độ fat points
regularity index
Hilbert function
coordinate ring
điểm béo
chỉ số chính quy
hàm Hilbert
vành tọa độ

How to Cite

1.
Thiện PV, Sinh TN, Quang NT. On the Castelnuovo-Mumford regularity index of the coordinate ring of a set of n + 3 non-degenerate fat points in projective space Pn. hueuni-jns [Internet]. 2021Jun.29 [cited 2021Oct.23];130(1C):15-22. Available from: http://jos.hueuni.edu.vn/index.php/hujos-ns/article/view/6334

Abstract

In this paper we calculate the Castelnuovo-Mumford regularity index of the coordinate ring of n + 3 a set of  non-degenerate fat points in Pn for almost all of cases.

https://doi.org/10.26459/hueunijns.v130i1C.6334
PDF (Vietnamese)

References

  1. Ballico E, Dumitrescu O, Postinghel E. On Segre's bound for fat points in Pn. Journal of Pure and Applied Algebra. 2016;220(6):2307-2323. DOI: https://doi.org/10.1016/j.jpaa.2015.11.008
  2. Catalisano MV, Trung NV, Valla G. A sharp bound for the regularity index of fat points in general position. Proceedings of The American Mathematical Scociety. 1993;18(3):717-724.
  3. Davis ED, Geramita AV. The Hilbert function of a special class of 1-dimensional Cohen - Macaulay graded algebras. The Curves Seminar at Queen’s, Queen’s Paper in Pure and Apply Mathematical. 1984;67:1-29.
  4. Fatabbi G, Lorenzini A. On a sharp bound for the regularity index of any set of fat points. Journal of Pure and Applied Algebra. 2001;161(1-2):91-111. DOI: https://doi.org/10.1016/s0022-4049(00)00083-9
  5. Nagel U, Trok B. Segre's regularity bound for fat point schemes. Annali della Scuola normale superiore di Pisa. Classe di scienze. 2020;20(1):217-237. DOI: https://doi.org/10.2422/2036-2145.201702_008
  6. Serge B. Alcune questioni su insiemi finiti di punti in geometria algebrica. Atti del convegno internazionale di Torino. 1961;67-85.
  7. Thien P.V. Serge bound for the regularity index of fat points in P3.Journal of Pure and Applied Algebra. 2000;151(2):197-214. DOI: https://doi.org/10.1016/s0022-4049(99)00055-9
  8. Thien PV. Regularity Index of S + 2 Fat Points not on a Linear (S − 1)-Space. Communications in Algebra. 2012;40(10):3704-3715. DOI: https://doi.org/10.1080/00927872.2011.
  9. Thien PV. Lower bound for the regularity index of fat points. International Journal of Pure and Apllied Mathematics. 2016;109(3):745-755. DOI: https://doi.org/10.12732/ijpam.v109i3.21
  10. Thien PV, Sinh TN. On the regularity index of s fat points not on a linear (r−1)-space, s ≤ r + 3. Communications in Algebra. 2016;45(10):4123-4138. DOI: https://doi.org/10.1080/00927872.2016.1222395
  11. Thien PV, Trinh TTV. An estimate of the regularity index of fat points in some cases. Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae, Sectio computatorica. 2019;49:399-410.
Creative Commons License

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Copyright (c) 2021 Array