Revista de Matemática: Teoría y Aplicaciones ISSN Impreso: 1409-2433 ISSN electrónico: 2215-3373

OAI: https://revistas.ucr.ac.cr/index.php/matematica/oai
On the F-pure threshold of the homogeneous maximal ideal of a Stanley-Reisner ring
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Keywords

Umbral F-puro
Anillos de Stanley–Reisner
Anillos de característica prima
F-pure threshold
Stanley-Reisner rings
Prime characteristic rings

How to Cite

Badilla-Céspedes, W. (2024). On the F-pure threshold of the homogeneous maximal ideal of a Stanley-Reisner ring. Revista De Matemática: Teoría Y Aplicaciones, 31(2), 153–165. https://doi.org/10.15517/rmta.v31i2.55788

Abstract

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.

https://doi.org/10.15517/rmta.v31i2.55788
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References

I. M. Aberbach y F. Enescu, The structure of F-pure rings. Math. Z. 250(2005), no. 4, 791-806. doi: 10.1007/s00209-005-0776-y

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

A. Benito, E. Faber y 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

M. Blickle, M. Mustata y K. E. 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

A. De Stefani y L. Núñez-Betancourt, F-thresholds of graded rings. Nagoya Math. J. 229(2018), 141-168. doi: 10.1017/nmj.2016.65

M. González Villa, D. Jaramillo-Velez y 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

N. Hara y 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

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

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

D. J. Hernández, K. Schwede, P. Teixeira y 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

M. Hochster y 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

M. Hochster y 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

C. Huneke, Tight closure and its applications. Vol. 88. Regional Conference Series in Mathematics. Conference Board of the Mathematical Sciences,1996.

C. Huneke y 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

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

E. Kunz, Characterizations of regular local rings for characteristic p. Amer. J. Math. 91(1969), 772-784. doi: 10.2307/2373351

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

M. Mustata, S. Takagi y K.-i. Watanabe, F-thresholds and Bernstein-Sato polynomials. European Congress of Mathematics. Eur. Math. Soc., Zürich, 2005, 341-364. doi: 10.48550/arXiv.math/0411170

T. Shibuta y S. Takagi, Log canonical thresholds of binomial ideals. Manuscripta Math. 130(2009), no. 1, 45-61. doi: 10.1007/s00229-009-0270-7

K. E. Smith y 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

S. Takagi y K.-i. Watanabe, On F-pure thresholds. J. Algebra 282(2004), no. 1, 278-297. doi: 10.1016/j.jalgebra.2004.07.011

K. Tucker, F-signature exists. Invent. Math. 190(2012), no. 3, 743-765. doi: 10.1007/s00222-012-0389-0

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

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