Deformations and smoothability of certain AS monomial curves
详细信息    查看全文
  • 作者:Anna Oneto (1)
    Grazia Tamone (1)
  • 关键词:Numerical semigroup ; Arithmetic sequence ; Monomial curve ; Deformation ; Weierstrass semigroup ; One ; point code ; Primary 14H55 ; Secondary 14H37 ; 11G20
  • 刊名:Beitr?ge zur Algebra und Geometrie / Contributions to Algebra and Geometry
  • 出版年:2014
  • 出版时间:October 2014
  • 年:2014
  • 卷:55
  • 期:2
  • 页码:557-575
  • 全文大小:258 KB
  • 参考文献:1. Buchweitz, R.O.: On Deformations of Monomial Curves. In: Par, M., Demazure et al. (ed.) Seminaire sur les Singularits des Surfaces, Centre de Math. de l鈥橢cole Polytechnique, Palaiseau, 1976/77. Springer Lecture Notes in Mathematics, vol. 777, pp. 205鈥?20. Springer, Berlin (1980)
    2. Buchsbaum, D.A., Eisenbud, D.: Algebra structures for finite free resolutions, and some structure theorems for ideals of codimension 3. Am. J. Math. 99(3) (1977)
    3. Del Centina, A.: Weierstrass points and their impact in the study of algebraic curves: a historical account from the 鈥?Luckensatz鈥?to the 1970s. Ann. Univ. Ferrara 54, 37鈥?9 (2008) CrossRef
    4. Eisenbud, D., Harris, H.: Existence, decomposition and limits of certain Weierstrass points. Invent. Math. 87, 495鈥?15 (1987) CrossRef
    5. Feng, G.L., Rao, T.R.N.: A simple approach for construction of algebraic-geometric codes from affine plane curves. IEEE Trans. Inf. Theory 40(4), 1003鈥?012 (1994) CrossRef
    6. Feng, G.L., Rao, T.R.N.: Decoding algebraic-geometric codes up to the designed minimum distance. IEEE Trans. Inf. Theory 39, 37鈥?5 (1993) CrossRef
    7. Gimenez, P., Sengupta, I., Srinivasan, H.: Minimal free resolutions for certain affine monomial curves. In: Corso, A., Polini, C. (eds.) Commutative Algebra and its Connections to Geometry, Contemporary Mathematics, vol. 555. American Mathematical Society, USA (2011)
    8. Hartshorne, R.: Algebraic Geometry, vol. 257. Springer, New York (1981)
    9. Hartshorne, R.: Deformation Theory, vol. 257. Springer, New York (2010)
    10. Hindry, M., Silverman, J.H.: Diophantine Geometry. An Introduction. In: Graduate Texts in Mathematics, vol. 201, Springer, Berlin (2000)
    11. H酶holdt, T., van Lint, J.H., Pellikaan, R.: Algebraic geometry of codes. Handbook of coding theory, vol. 1, pp. 871鈥?61. Elsevier, Amsterdam (1998)
    12. Kim, S.J.: Semigroups which are not Weiestrass semigroups. Bull Korean Math. Soc. 33(2), 187鈥?91 (1996) CrossRef
    13. Komeda, J.: On Weierstrass points whose first non gaps are four. J. Reine Angew Math 341, 68鈥?6 (1983)
    14. Komeda, J.: On the existence of Weierstrass points whose first non gaps are five. Manuscripta Math. 76 (1992)
    15. Komeda, J.: On the existence of Weierstrass gap sequences on curves of genus \(\le 8\) . JPAA 97, 51鈥?1 (1994)
    16. Komeda, J.: Existence of the primitive Weiestrass gap sequences on curve of genus 9. Boll. Soc. Brasil. Math. 30(2), 125鈥?37 (1999) CrossRef
    17. Kurano, K.: The first Syzygies of determinantal ideals. J. Algebra 124, 414鈥?36 (1989) CrossRef
    18. Maclachlan, C.: Weierstrass points on compact Riemann surfaces. J. London Math. Soc. 2(3), 722鈥?24 (1971) CrossRef
    19. Matsumura, H.: Commutative Algebra. W.A. Benjamin Co, New York (1970)
    20. Oliveira, G.: Weierstrass semigroups and the canonical ideal of non-trigonal curves. Manuscripta mathematica 71, 431鈥?50 (1991) CrossRef
    21. Oneto, A., Tamone, G.: On some invariants in numerical semigroups and estimations of the order bound. Semigroup Forum 81(3), 483鈥?09 (2010) CrossRef
    22. Oneto, A., Tamone, G.: Smoothability and order bound for AS semigroups. Semigroup Forum 85(2), 268鈥?88 (2012) CrossRef
    23. Patil, D., Tamone, G.: On the h-polynomial of certain monomial curves. Rocky Mt. J. Math. 34(1), 289鈥?07 (2004) CrossRef
    24. Pinkham, H.C.: Deformations of algebraic varieties with \(G_m\) action. Asterisque 20, (1974)
    25. Rim, D.S., Vitulli, M.A.: Weierstrass points and monomial curves. J. Algebra 48, 454鈥?76 (1977) CrossRef
    26. Robbiano, L.: Coni tangenti e singolarit脿 razionali. Curve algebriche- istituto di Analisi Globale, Firenze (1981)
    27. Schaps, M.: Deformations of Cohen-Macaulay schemes of codimension 2 and non-singular deformations of space curves. Am. J. Math. 99, 669鈥?85 (1975) CrossRef
    28. Schaps, M.: Nonsingular deformations of a determinantal scheme. Pac. J. Math. 65(1), 209鈥?15 (1976) CrossRef
    29. Schlessinger, M.: Functors of Artin rings. Trans. Am. Math. Soc 130 (1968)
    30. Sengupta, I.: A Grobner basis for certain affine monomial curves. Comm. Algebra 31(3), 1113鈥?129 (2003) CrossRef
    31. Sharifan, L., Zaare-Nahandi, R.: Minimal free resolutions of the associated graded ring of monomial curves of generalized arithmetic sequences. JPAA 213(3), 360鈥?69 (2009)
    32. Stevens, J.: Deformations of Singularities. In: Lecture Notes in Math, vol. 1811. Springer, Berlin (2003)
    33. Torres, F.: Weierstrass points and double coverings of curves. Manuscripta Math. 83, 39鈥?8 (1994) CrossRef
  • 作者单位:Anna Oneto (1)
    Grazia Tamone (1)

    1. Dima, University of Genova, via Dodecaneso 35, 16146聽, Genoa, Italy
  • ISSN:2191-0383
文摘
In this paper, we consider semigroups of embedding dimension five generated by arithmetic sequences. We prove these semigroups are Weierstrass by showing that the associated monomial curves are smoothable.
NGLC 2004-2010.National Geological Library of China All Rights Reserved.
Add:29 Xueyuan Rd,Haidian District,Beijing,PRC. Mail Add: 8324 mailbox 100083
For exchange or info please contact us via email.