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Birational geometry of complete intersections. (English) Zbl 0907.14023
Let \(Y\subset \mathbb{P}^n\) be a smooth complete intersection. The author studies the cohomology groups of symmetric differential forms \(S^r \Omega^1_Y\) on \(Y\). Some vanishing theorems and explicit formulas for \(\dim H^q(Y,S^r\Omega^1_Y)\) are proved. In particular, it is shown that the birational invariants \(\dim H^0 (Y,S^r \Omega^1_Y \otimes \omega^s_Y)\) are independent of classical invariants.

MSC:
14M10 Complete intersections
14E05 Rational and birational maps
14F17 Vanishing theorems in algebraic geometry
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