Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 113 / 4 / c / iv

Solution

0 < i < dim Y = r - 1

H^{i} (X, O_{X} (n)) ⟶ H^{i} (Y, O_{Y} (n)) ⟶ H^{i + 1} (X, O_{X} (n - d)) .

Both outer terms are intermediate cohomology groups on

P_{k}^{r}

, because

1 \leq i < i + 1 \leq r - 1

H^{i} (Y, O_{Y} (n)) = 0 (0 < i < dim Y, n \in Z) .

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