Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 4 / 24F / a / ii

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- Solution ii

Solution

The Adjunction formula gives

K_{X} ≅ O_{X} (d - 3)

. Since a hyperplane section has degree

d

, the canonical degree of a smooth plane curve is

de g K_{X} = d (d - 3) .

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