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 Incoming links: Self-intersection of a smooth curve on a K3 surface

Past exam of the mathematics course of the University of Cambridge / 2009 / iii / Paper 20 / 4 / ii / Solution Created 2026-10-03 Updated 2026-10-14

The canonical bundle of a K3 surface is trivial, so

c_{1} (TX) = 0

. Apply the adjunction formula with

g = 3

:

Σ \cdot Σ = 2 \cdot 3 - 2 = 4.

This is the Self-intersection of a smooth curve on a K3 surface.

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