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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.

##### MSC:
 14M10 Complete intersections 14F17 Vanishing theorems in algebraic geometry 14E05 Rational and birational maps 14M17 Homogeneous spaces and generalizations
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##### References:
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