Spanish (pdf)
Article in xml format
Article references
Automatic translation
Send this article by e-mail
Permalink
Mathematics Subject Classification: Primary: 13A35, 13F55; Secondary: 14B05.
Ver contenido completo en PDF.
Services on Demand
Journal
Article
Indicators
-
Cited by SciELO -
Access statistics
Related links
-
Similars in
SciELO
Share
Revista de Matemática Teoría y Aplicaciones
Print version ISSN 1409-2433
Rev. Mat vol.31 n.2 San José Jul./Dec. 2024
http://dx.doi.org/10.15517/rmta.v31i2.55788
Artículo
Sobre el umbral F-puro del ideal homogéneo máximo de un anillo de Stanley-Reisner
On the F-pure threshold of the homogeneous maximal ideal of a Stanley-Reisner ring
1Universidad Nacional Autónoma de México, Centro de Ciencias Matemáticas, Morelia, México; wagner@matmor.unam.mx
En característica prima, el umbral F-puro es un invariante numérico que mide singularidades. Se conocen pocas estimaciones de este número. En esta nota, calculamos explícitamente el umbral F-puro del ideal homogéneo máximo en un anillo de Stanley-Reisner y demostramos que este número y la dimensión de escisión son iguales.
Palabras clave: Umbral F-puro; Anillos de Stanley-Reisner; Anillos de característica prima.
In prime characteristic, the F-pure threshold is a numerical invariant measuring singularities. Few estimates of this number are known. In this note, we explicitly compute the F-pure threshold of the homogeneous maximal ideal in a Stanley-Reisner ring and prove that this number and the splitting dimension are same.
Keywords: F-pure threshold; Stanley-Reisner rings; Prime characteristic rings.
Agradecimientos
El autor agradece a Luis Núñez-Betancourt por sus útiles comentarios y sugerencias. También agradece al árbitro anónimo por sus útiles comentarios. El autor hizo este trabajo durante una estancia posdoctoral realizada gracias al Programa de Becas Posdoctorales en la UNAM (POSDOC).
Referencias
I,M, Aberbach; F, Enescu. The structure of F-pure rings. Math. Z. 250(2005), no. 4, 791-806. doi: 10.1007/s00209-005-0776-y [ Links ]
W, Badilla-Céspedes. F-invariants of Stanley-Reisner rings. J. Pure Appl. Algebra 225(2021), no. 9, Paper No. 106671, 19. doi: 10.1016/j.jpaa.2021.106671 [ Links ]
A, Benito; E, Faber; K,E, Smith. Measuring singularities with Frobenius: the basics. Commutative algebra. Springer, New York, 2013, 57-97. doi: 10.1007/978-1-4614-5292-8_3 [ Links ]
M, Blickle; M, Mustata; KE, Smith. Discreteness and rationality of Fthresholds. Michigan Math. J. 57(2008). Special volume in honor of Melvin Hochster, 43-61. doi: 10.1307/mmj/1220879396 [ Links ]
A, De Stefani; L, Núñez-Betancourt. F-thresholds of graded rings. Nagoya Math. J.229(2018), 141-168. doi: 10.1017/nmj.2016.65 [ Links ]
M, González Villa; D, Jaramillo-Velez; L, Núñez-Betancourt. F-thresholds and test ideals of Thom-Sebastiani type polynomials. Proc. Amer. Math. Soc. 150(2022), no. 9, 3739-3755. doi: 10.1090/proc/16025 [ Links ]
N, Hará; K,I, Yoshida. A generalization of tight closure and multiplier ideals. Trans. Amer. Math. Soc. 355(2003), no. 8, 3143-3174. doi: 10.1090/S0002-9947-03-03285-9 [ Links ]
D,J, Hernández. F-pure thresholds of binomial hypersurfaces. Proc. Amer. Math. Soc. 142(2014), no. 7, 2227-2242. doi: 10.1090/S0002- 9939- 2014-11941-1 [ Links ]
D,J, Hernández. F-purity versus log canonicity for polynomials. Nagoya Math. J. 224(2016), no. 1, 10-36. doi: 10.1017/nmj.2016.14 [ Links ]
D,J, Hernández; K, Schwede; P, Teixeira; E,E, Witt. The FrobeniusThresholds package for Macaulay2. J. Softw. Algebra Geom. 11(2021), no. 1, 25-39. doi: 10.2140/jsag.2021.11.25 [ Links ]
M, Hochster; C, Huneke. Tight closure, invariant theory, and the Briancon-Skoda theorem. J. Amer. Math. Soc. 3(1990), no. 1, 31-116. doi: 10.2307/1990984 [ Links ]
M, Hochster; J,L, Roberts. The purity of the Frobenius and local cohomology. Advances in Math. 21(1976), no. 2, 117-172. doi: 10.1016/0001-8708(76)90073-6 [ Links ]
C, Huneke. Tight closure and its applications. Vol. 88. Regional Conference Series in Mathematics. Conference Board of the Mathematical Sciences, 1996. [ Links ]
C, Huneke; G,J, Leuschke. Two theorems about maximal Cohen-Macaulay modules. Math. Ann. 324(2002), no. 2, 391-404. doi: 10.1007/s00208-002-0343-3 [ Links ]
Z, Kadyrsizova; et al. Lower bounds on the F-pure threshold and extremal singularities. Trans. Amer. Math. Soc. Ser. B 9(2022), 977-1005. doi: 10.1090/btran/106 [ Links ]
E, Kunz. Characterizations of regular local rings for characteristic p. Amer. J. Math. 91(1969), 772-784. doi: 10.2307/2373351 [ Links ]
S, Müller. The F-pure threshold of quasi-homogeneous polynomials. J. Pure Appl. Algebra 222(2018), no. 1, 75-96. doi: 10.1016/j.jpaa.2017.03.005 [ Links ]
M, Mustata; S, Takagi; Ki, Watanabe. F-thresholds and Bernstein-Sato polynomials. European Congress of Mathematics. Eur. Math. Soc., Zürich, 2005, 341-364. doi: 10.48550/arXiv.math/0411170 [ Links ]
T, Shibuta; S, Takagi. Log canonical thresholds of binomial ideals. Manuscripta Math. 130(2009), no. 1, 45-61. doi: 10.1007/s00229-009-0270-7 [ Links ]
K,E, Smith; M, Van den Bergh. Simplicity of rings of differential operators in prime characteristic. Proc. London Math. Soc. (3) 75(1997), no. 1, 32-62. doi: 10.1112/S0024611597000257 [ Links ]
S, Takagi; Ki, Watanabe. On F-pure thresholds. J. Algebra 282(2004), no. 1, 278-297. doi: 10.1016/j.jalgebra.2004.07.011 [ Links ]
K, Tucker. F-signature exists. Invent. Math. 190(2012), no. 3, 743-765. doi: 10.1007/s00222-012-0389-0 [ Links ]
Y, Yao. Observations on the F-signature of local rings of characteristic p. J. Algebra 299(2006), no. 1, 198-218. doi: 10.1016/j.jalgebra.2005.08.013 [ Links ]
Recibido: 03 de Agosto de 2023; Aprobado: 16 de Mayo de 2024
This is an open-access article distributed under the terms of the Creative Commons Attribution License
