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Generic hyperplane section of a projective curve

For a general linear form

ℓ

not vanishing identically on a projective curve, the exact sequence

0 \to A_{C} (- 1) ℓ A_{C} \to A_{C} / (ℓ) \to 0

shows that the hyperplane-section length is

P_{C} (m) - P_{C} (m - 1) = de g C

.

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