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Canonical map of a hyperelliptic curve

The canonical map of an even-degree hyperelliptic curve is

(x, y) ⟼ [1 : x : \dots : x^{n - 2}],

so it identifies the two points

(x, y)

and

(x, - y)

of a general fibre and is not an embedding.

 Ancestors (8)

 Incoming links (1)

Solution