Reduced Weighted Complete Intersection and Derivations Original Research Article

LetA=image[x1,…,xn]/(f1,…,fn) be a zero-dimensional weighted complete intersection (char image=0). We prove a general result on the (homogeneous) derivations ofA. In particular we deduce that in the “generic” case when image[x1,…,xn]/(f1,…,fn−1) is reduced (deg(fi)≤deg(fn), i=1,…,n−1) there are no nontrivial derivations of strictly negative degree. If moreover all the weights of the variablesxiare even it follows that the Serre spectral sequence of any orientable fibrationFright arrow-hookedE→B, withH*F=Aas graded algebras, collapses at theE2-term, thus verifying a conjecture of Halperin. We also discuss several examples.