Abstract
Using the finite determinacy relation with the regular sequence in the Ring Theory and the complete intersection in Analytic Geometry, the finite indeterminacy of homogeneous polynomial germs under some subgroupsR R r ofR in both real and complex case is proven by the homogeneity of the polynomial germs. It results in the finite determinacy of homogeneous polynomial germs needn’t be discussed respectively.
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References
Zhang Guo-bin. Finite Determinacy of Smooth Map-germ (II):M-A k-Determinacy.Acta Math Sinica, 1990,33(1): 34–42 (Ch).
Zhang Guo-bin. Finite Determinacy of Smooth map-germ (III):M-R k-Determinacy.Acta Math Sinica, 1991,34 (1):111–117 (Ch).
Li Yang-cheng. On the Estimates of the Order of Finitely-A k-Determinedmap-Germs.Acta Math Sinica, 1988,4 (1):28–38.
Wall C T C. Finite Determinacy of Smooth Map-Germs.Bull London Math Soc 1981,13, 481–539.
du Plessis A. On the Determinacy of Smooth Map-Germs.Invent Math, 198058:107–160.
Xiong Jian-fei. On the Finite Determinacy of Smooth Map-Germs Under some Subgroups ofA andK.Jour Math Rsearch and Exposition, 1999,19 (2): 439–444 (Ch).
Alexandru Dimca.Topics on Real and Complex Singularites. Wiesbaden: Friedr Vieweg & Sohn Braunschweig, 1987.
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Foundation item: Supported by the National Nature Science Foundation of China(10261002)
Biography: LIU Heng-xing(1961-), male, Ph.D. candidate, Associate professor, research direction: singularity theory.
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Heng-xing, L., Dun-mu, Z. Finite indeterminacy of homogenous polynomial germs under some subgroupsR I r ofR . Wuhan Univ. J. Nat. Sci. 10, 803–807 (2005). https://doi.org/10.1007/BF02832416
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DOI: https://doi.org/10.1007/BF02832416