an:00977870
Zbl 0907.14023
Rackwitz, H.-G.
Birational geometry of complete intersections
EN
Abh. Math. Semin. Univ. Hamb. 66, 263-271 (1996).
00037817
1996
j
14M10 14E05 14F17
complete intersection; symmetric differential forms; vanishing theorems; birational invariants
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.
Yuri G.Prokhorov (MR 97g:14016)