Projective dimension of second order symmetric derivation of Kahler modules for hypersurfaces

摘要

$R = k[x_1,...,x_s]$ be a polynomial algebra and I be an ideal of R generated by $f in R.$ Then $S=R/I=rac{k[x_1,...,x_s]}{(f)} $ be an affine domain which is called hypersurfaces. $Omega_1(S)$ denotes the module of first order derivations of K"{a}hler modules over S. $ee^2 (Omega_1(S))$ denotes the module of second order derivations of symmetric algebra on $Omega_1(S).$ In this paper, we prove that if S be an affine domain represented by $ S=rac{k[x_1,...,x_s]}{(f)}$, then projective dimension of $ee^2(Omega_1(S))$ is less than or equal to 1.