L-valued 1-jet de Rham complexes and their induced spectral sequences (Q752560)

Let M be a compact, complex manifold, E a holomorphic vector bundle of rank r over M and \(L=Op(E)(1)\) the tautological line bundle of the projective bundle f: P(E)\(=(E^{\vee}-\{0\}/{\mathbb{C}}^*)\to M\). The author considers the sheaves of L-valued 1-jet forms on the projective bundle P(E) and makes them into a complex defining a suitable differential operator of first order by means of a global section of E. Then he constructs a double spectral sequence from ``E-valued'' cohomology, \(H^ p(M,\Omega^ p_ m(E))\) to topological cohomology of these complexes. The differential operator considered by the author is basically the one introduced by \textit{A. Ogus} in 1976 [Am. J. Math. 97(1975), 1085-1107 (1976; Zbl 0331.14002)].