1
School of Mathematics and Statistics,Wuhan University, Wuhan, assistance professor
2
School of Mathematics and Statistics, Wuhan University, P.O. Box 430072, Wuhan, People's Republic of China
Abstract
For singularities $fin K[[x_{1},ldots,x_{n}]]$ over an algebraically closed field $K$ of arbitrary characteristic, we introduce the finite $\mathcal{S}-$determinacy under $\mathcal{S}-$equivalence, where $\mathcal{S}=\mathcal{R}_{\mathcal{G}},~\mathcal{R}_{\mathcal{A}}, ~\mathcal{K}_{\mathcal{G}},~\mathcal{K}_{\mathcal{A}}$. It is proved that the finite $\mathcal{R}_{\mathcal{G}}(\mathcal{K}_{\mathcal{G}})-$determinacy is equivalent to the finiteness of the relative $\mathcal{G}-$Milnor ($\mathcal{G}-$Tjurina) number and the finite $\mathcal{R}_{\mathcal{A}}(\mathcal{K}_{\mathcal{A}})-$determinacy is equivalent to the finiteness of the relative $\mathcal{A}-$Milnor ($\mathcal{A}-$Tjurina) number. Moreover, some estimates are provided on the degree of the $\mathcal{S}-$determinacy in positive characteristic.
Hengxing, L., & Jingwen, L. &. (2014). The finite $S$-determinacy of singularities in positive characteristic $S=R_G,R_A, K_G,K_A$. Bulletin of the Iranian Mathematical Society, 40(6), 1347-1372.
MLA
Hengxing, L., & Jingwen, L. &. "The finite $S$-determinacy of singularities in positive characteristic $S=R_G,R_A, K_G,K_A$", Bulletin of the Iranian Mathematical Society, 40, 6, 2014, 1347-1372.
HARVARD
Hengxing L., Jingwen L. &. (2014). 'The finite $S$-determinacy of singularities in positive characteristic $S=R_G,R_A, K_G,K_A$', Bulletin of the Iranian Mathematical Society, 40(6), pp. 1347-1372.
CHICAGO
L. Hengxing & L. &. Jingwen, "The finite $S$-determinacy of singularities in positive characteristic $S=R_G,R_A, K_G,K_A$," Bulletin of the Iranian Mathematical Society, 40 6 (2014): 1347-1372,
VANCOUVER
Hengxing L., Jingwen L. &. The finite $S$-determinacy of singularities in positive characteristic $S=R_G,R_A, K_G,K_A$. BIMS. 2014;40(6):1347-1372.
