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Vietnam Journal of Mathematics 33:3 (2005) 271-281

A Presentation of the Elements of the Quotient Sheaves $\Omega^k_r/\Theta^k_r$ in Variational Sequences

Nong Quoc Chinh

Abstract. In this paper we give a concrete presentation of the elements of the quotient sheaves $ \Omega^k_r/\Theta^k_r$ in the variational sequence $$0\rightarrow R\rightarrow \Omega^0_r\overset{E_0}{rightarrow} \Omega^1_r/\Theta^1_r\overset{E_1}{\rightarrow} \Omega^2_r\/Theta^2_r \overset{E_2}{\rightarrow}\ldots \overset{E_{P-1}}{\rightarrow}\Omega^{P-1}_r/\Theta^{P-1}_r\rightarrow$$ $$\overset{E_{p-1}}{\rightarrow}\Omega^P_r/\Theta^P_r \overset{E_P}{\rightarrow}\Omega^{P+1}_r \overset{E_{P+1}}{\rightarrow} \ldots \rightarrow \Omega^N_r \rightarrow 0.$$