# IJPAM: Volume 46, No. 1 (2008)

-SYMMETRICAL TENSOR DIFFERENTIAL FORMS WITH
LOGARITHMIC POLES ALONG A HYPERSURFACE SECTION

Peter Brückmann, Patrick Winkert
Department of Mathematics
Martin-Luther-University
Wittenberg, Halle, 06099, GERMANY
e-mail: brueckmann@mathematik.uni-halle.de
e-mail: patrick.winkert@mathematik.uni-halle.de

Abstract.The aim of this paper is to investigate -symmetrical tensor differential forms with logarithmic poles on the projective space and on complete intersections . Let , be a nonsingular irreducible algebraic hypersurface which implies that is a prime divisor in . The main goal of this paper is the study of the locally free sheaves and the calculation of their cohomology groups. In addition, for complete intersections we give some vanishing theorems and recursion formulas.