46
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Multiplier ideals of plane curve singularities via Newton polygons

ORCID Icon, ORCID Icon, &
Pages 1142-1162 | Received 21 Jun 2022, Accepted 01 Sep 2023, Published online: 22 Sep 2023

References

  • Alberich-Carramiñana, M., Álvarez Montaner, J., Dachs-Cadefau, F. (2016). Multiplier ideals in two-dimensional local rings with rational singularities. Michigan Math. J. 65(2):287–320. DOI: 10.1307/mmj/1465329014.
  • Alberich-Carramiñana, M., Álvarez Montaner, J., Blanco, G. (2021). Monomial generators of complete planar ideals. J. Algebra Appl. 20(3):Article 2150032. DOI: 10.1142/S0219498821500328.
  • A’Campo, N., Oka, M. (1996). Geometry of plane curves via Tschirnhausen resolution tower. Osaka J. Math. 33(4):1003–1033.
  • Berkesch, C., Leykin, A. (2010). Algorithms for Bernstein–Sato polynomials and multiplier ideals. Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation. New York, NY: Association for Computing Machinery, pp. 99–106.
  • Budur, N. (2012). Singularity invariants related to Milnor fibers: survey. In: Campillo, A., Cardona, G., Melle-Hernández, A., Veys, W., Zúñiga-Galindo, A., eds. Zeta Functions in Algebra and Geometry. Contemporary Mathematics, Vol. 566. Providence, RI: American Mathematical Society, pp. 161–187.
  • Campillo. A., Galindo, C. (2003). The Poincaré series associated with finitely many monomial valuations. Math. Proc. Cambridge Philos. Soc. 134(3):433–443. DOI: 10.1017/S030500410200645X.
  • Cox, D. A., Little, J. B., Schenck, H. K. (2011). Toric varieties. Graduate Studies in Mathematics, Vol. 124. Providence, RI: American Mathematical Society.
  • Cassou-Noguès, Pi., Libgober, A. (2014). Multivariable Hodge theoretical invariants of germs of plane curves. II. In: Campillo, A., Kuhlmann, F.-V., Teissier, B., eds. Valuation Theory in Interaction. EMS Ser. Congr. Rep. Zürich: European Mathematical Society, pp. 82–135.
  • Delgado, F., Galindo, C., Núñez, A. (2008). Generating sequences and Poincaré series for a finite set of plane divisorial valuations. Adv. Math. 219(5):1632–1655. DOI: 10.1016/j.aim.2008.06.017.
  • Dũng Tráng, L., Oka, M. (1995). On resolution complexity of plane curves. Kodai Math. J. 18(1):1–36.
  • Ein, L., Lazarsfeld, R., Smith, K. E., Varolin, D. (2004). Jumping coefficients of multiplier ideals. Duke Math. J. 123(3):469–506. DOI: 10.1215/S0012-7094-04-12333-4.
  • Ewald, G. (1996). Combinatorial Convexity and Algebraic Geometry. New York, NY: Springer-Verlag.
  • Favre, C., Jonsson, M. (2004). The valuative tree, Lecture Notes in Mathematics, Vol. 1853. Berlin: Springer-Verlag.
  • Favre, C., Jonsson, M. (2005). Valuations and multiplier ideals. J. Amer. Math. Soc. 18(3):655–684. DOI: 10.1090/S0894-0347-05-00481-9.
  • Fulton, W. (2016). Introduction to Toric Varieties. Annals of Mathematics Studies, Vol. 131. Princeton: Princeton University Press.
  • Guzmán Durán, C. R. (2018). Ideales multiplicadores de curvas planas irreducibles. Ph.D. dissertation. Centro de investigación en matemáticas, Guanajuato, Mexico. http://cimat.repositorioinstitucional.mx/jspui/handle/1008/725
  • García Barroso, E. R., González Perez, P. D., Popescu-Pampu, P. (2019). The valuative tree is the projective limit of Eggers-Wall trees. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM. 113(4):4051–4105. DOI: 10.1007/s13398-019-00646-z.
  • García Barroso, E. R., González Perez, P. D., Popescu-Pampu, P. (2020). The combinatorics of plane curve singularities. How Newton polygons blossom into lotuses. In: Cisneros-Molina, J. L., Dung Tráng, L., Seade, J., eds. Handbook of Geometry and Topology of Singularities I. Cham: Springer, pp. 1–150.
  • González Pérez, P. D. (2003). Toric embedded resolutions of quasi-ordinary hypersurface singularities. Ann. Inst. Fourier (Grenoble). 53(6):1819–1881. DOI: 10.5802/aif.1993.
  • Hyry, E., Järvilehto, T. (2011). Jumping numbers and ordered tree structures on the dual graph. Manuscripta Math. 136(3):411–437. DOI: 10.1007/s00229-011-0449-6.
  • Hyry, E., Järvilehto, T. (2018). A formula for jumping numbers in a two-dimensional regular local ring. J. Algebra 516:437–470. DOI: 10.1016/j.jalgebra.2018.09.016.
  • Howald, J. A. (2001). Multiplier ideals of monomial ideals. Trans. Amer. Math. Soc. 353(7):2665–2671. DOI: 10.1090/S0002-9947-01-02720-9.
  • Howald, J. A. (2003). Multiplier ideals of sufficiently general polynomials. arXiv:math/0303203 [math.AG].
  • Järvilehto, T. (2011). Jumping numbers of a simple complete ideal in a two-dimensional regular local ring. Mem. Amer. Math. Soc. 214:78. DOI: 10.1090/S0065-9266-2011-00597-6.
  • Jonsson, M. (2015). Dynamics on Berkovich spaces in low dimensions. In: Ducros, A., Favre, C., Nicaise, J., eds. Berkovich Spaces and Applications. Lecture Notes in Math., Vol. 2119. Cham: Springer, pp. 205–366.
  • Lazarsfeld, R. (2004). Positivity in algebraic geometry. II. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge, Vol. 49. Heidelberg, Berlin: Springer.
  • Naie, D. (2009). Jumping numbers of a unibranch curve on a smooth surface. Manuscripta Math. 128(1):33–49. DOI: 10.1007/s00229-008-0223-6.
  • Lê, D. T., Oka, M., (1995). On resolution complexity of plane curves. Kodai Math. J. 18(1):1–36 DOI: 10.2996/kmj/1138043350.
  • Oda, T. (1988). Convex Bodies and Algebraic Geometry. Ergebnisse der Mathematik und ihrer Grenzgebiete (3), Vol. 15. Berlin: Springer-Verlag.
  • Oka, M. (1996). Geometry of plane curves via toroidal resolution. In: Campillo López, A., Narváez Macarro, L., eds. Algebraic Geometry and Singularities. Basel: Birkhäuser, pp. 95–121.
  • Robredo Buces, M. (2019). Invariants of singularities, generating sequences and toroidal structures. Ph.D. dissertation. Universidad Complutense de Madrid, Madrid, Spain. https://www.icmat.es/Thesis/2019/Tesis_Miguel_Robredo.pdf
  • Shibuta, T. (2011). Algorithms for computing multiplier ideals. J. Pure Appl. Algebra 215(12):2829–2842. DOI: 10.1016/j.jpaa.2011.04.002.
  • Spivakovsky, M. (1990). Valuations in function fields of surfaces. Amer. J. Math. 112(1):107–156. DOI: 10.2307/2374856.
  • Smith, K. E., Thompson, H. M. (2007). Irrelevant exceptional divisors for curves on a smooth surface. In: Corso, A., Migliore, J, Polini, C., eds. Algebra, Geometry and their Interactions. Contemporary Mathematics, Vol. 448. Providence, RI: American Mathematical Society, 245–254.
  • Schwede, K., Tucker, K. (2012). A survey of test ideals. In: Francisco, C., Klingler, L., Sather-Wagstaff, S., Vassilev, J. C. eds. Progress in Commutative Algebra 2. Berlin: Walter de Gruyter, pp. 39–99.
  • Tucker, K. (2010). Jumping numbers and multiplier ideals on algebraic surfaces. Ph.D. dissertation. University of Michigan, Ann Arbor, MI: ProQuest LLC.
  • Tucker, K. (2010). Jumping numbers on algebraic surfaces with rational singularities. Trans. Amer. Math. Soc. 362(6):3223–3241. DOI: 10.1090/S0002-9947-09-04956-3.
  • Zhang, M. (2019). Multiplier ideals of analytically irreducible plane curves. arXiv:1907.06281v3 [math.AG].

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.