Abstract
Algebraic local cohomology classes attached to semi-quasiho-mogeneous hypersurface isolated singularities are considered. A new algorithm, that utilizes local cohomology classes with parameter, is proposed to compute Tjurina stratifications associated with μ-constant deformations of weighted homogeneous isolated singularities. The proposed algorithm has been implemented in a computer algebra system. Usage of the implementation is also described.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Arnold, V.I.: Normal forms of functions in neighbourhoods of degenerate critical points. Russian Math. Survey 29, 10–50 (1974)
Grothendieck, A.: Local Cohomology, notes by R. Hartshorne. Lecture Notes in Math., vol. 41. Springer (1967)
Martin, B., Pfister, G.: The kernel of the Kodaira-Spencer map of the versal μ-constant deformation of an irreducible plane curve with C ∗ -action. Journal of Symbolic Computation 7, 527–531 (1989)
Nabeshima, K., Tajima, S.: On efficient algorithms for computing parametric local cohomology classes associated with semi-quasihomogeneous singularities and standard bases. In: Proc. ISSAC 2014, pp. 351–358. ACM-Press (2014)
Nakamura, Y., Tajima, S.: On weighted-degrees for algebraic local cohomologies associated with semi-quasihomogeneous singularities. Advanced Studies in Pure Mathematics 46, 105–117 (2007)
Nakamura, Y., Tajima, S.: Algebraic local cohomologies and local b-functions Attached to semi-quasihomogeneous singularities with L(f) = 2. IRMA Lectures in Mathematics and Theoretical Physics 20, 103–116 (2012)
Noro, M., Takeshima, T.: Risa/Asir- A computer algebra system. In: Proc. ISSAC 1992, pp. 387–396. ACM-Press (1992)
Saito, K.: Quasihomogeneous isolated Singularitäten von Hyperflächen. Invent. Math. 14, 123–142 (1971)
Tajima, S.: Parametric local cohomology classes and Tjurina stratifications for μ-constant deformations of quasi-homogeneous singularities. In: Topics on Real and Complex Singularities, pp. 189–200. World Scientific (2014)
Tajima, S., Nakamura, Y.: Algebraic local cohomology class attached to quasi-homogeneous isolated hypersurface singularities. Publications of the Research Institute for Mathematical Sciences 41, 1–10 (2005)
Tajima, S., Nakamura, Y.: Annihilating ideals for an algebraic local cohomology class. Journal of Symbolic Computation 44, 435–448 (2009)
Tajima, S., Nakamura, Y.: Algebraic local cohomology classes attached to unimodal singularities. Publications of the Research Institute for Mathematical Sciences 48, 21–43 (2012)
Tajima, S., Nakamura, Y., Nabeshima, K.: Standard bases and algebraic local cohomology for zero dimensional ideals. Advanced Studies in Pure Mathematics 56, 341–361 (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Nabeshima, K., Tajima, S. (2014). An Algorithm for Computing Tjurina Stratifications of μ-Constant Deformations by Using Local Cohomology Classes with Parameters. In: Hong, H., Yap, C. (eds) Mathematical Software – ICMS 2014. ICMS 2014. Lecture Notes in Computer Science, vol 8592. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44199-2_79
Download citation
DOI: https://doi.org/10.1007/978-3-662-44199-2_79
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-44198-5
Online ISBN: 978-3-662-44199-2
eBook Packages: Computer ScienceComputer Science (R0)