IJPAM: Volume 46, No. 1 (2008)

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

Peter Brückmann$^1$, Patrick Winkert$^2$
$^{1,2}$Department of Mathematics
Martin-Luther-University
Wittenberg, Halle, 06099, GERMANY
$^1$e-mail: brueckmann@mathematik.uni-halle.de
$^2$e-mail: patrick.winkert@mathematik.uni-halle.de


Abstract.The aim of this paper is to investigate $T$-symmetrical tensor differential forms with logarithmic poles on the projective space $\PN$ and on complete intersections $Y \subset \PN$. Let $H \subset \PN, N\geq 2$, be a nonsingular irreducible algebraic hypersurface which implies that $D=H$ is a prime divisor in $\PN$. The main goal of this paper is the study of the locally free sheaves $\Om^T_{\PN}(\log D)$ and the calculation of their cohomology groups. In addition, for complete intersections $Y \subset \PN$ we give some vanishing theorems and recursion formulas.

Received: April 25, 2008

AMS Subject Classification: 14F10, 14M10, 14F17, 55N30

Key Words and Phrases: Young tableaux, complete intersections, algebraic differential forms

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 46
Issue: 1