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\(T\)-symmetrical tensor forms on complete intersections. (English) Zbl 0724.14032
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.

14M10 Complete intersections
14F17 Vanishing theorems in algebraic geometry
14E05 Rational and birational maps
14M17 Homogeneous spaces and generalizations
Full Text: DOI EuDML
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