 Singular locus of a product with a smooth variety

ID: singular-locus-of-a-product-with-a-smooth-variety

Codex  0 Created 2026-09-24 Updated 2026-09-24

Since

T_{(x, y)} (X \times Y) = T_{x} X \oplus T_{y} Y

, if

Y

is smooth then

Sing (X \times Y) = Sing (X) \times Y .

In particular, dimensions add.

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