an:04193897
Zbl 0724.14032
Br??ckmann, P.; Rackwitz, H.-G.
\(T\)-symmetrical tensor forms on complete intersections
EN
Math. Ann. 288, No. 4, 627-635 (1990).
00156123
1990
j
14M10 14F17 14E05 14M17
tensor product of sheaf of regular 1-forms; Young tableau; vanishing theorems; complete intersection; Lefschetz type theorems
Let \(\Omega^ 1\) be the sheaf of regular 1-forms over a smooth projective variety V and let \({\mathcal T}^ r=\otimes^{r}_{1}\Omega^ 1 \) be its r-th tensor product. The authors consider a splitting of \({\mathcal T}^ r\) into the direct sum \({\mathcal T}^ r=\oplus {\mathcal T}^ T \) of subsheaves \({\mathcal T}^ T\) where each \({\mathcal T}^ T\) is assigned to a standard Young tableau with r cells (these tableaux are connected with irreducible representations of the symmetric group \(S_ r).\)
The main results of the paper are some vanishing theorems for the cohomology groups of a smooth complete intersection Y with coefficients in the twisted sheaves \({\mathcal T}^ T(p)\). - Besides, there are some Lefschetz type theorems concerning the restrictions of tensor forms on the section by hypersurfaces.
T.Krasi??ski (????d??)