ScalingStacks

Remark 1.1.4 . [04Z3]

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Remark 1.1.4.

Transverse to the divisor H⊂DH\subset D, the singular fibration ℱt\mathcal{F}_{t} is topologically modeled on the composition of the Hopf fibration

ℂ2→ℂ⊕ℝ≃ℝ3;(z1,z2)↦(z1​z2,12​(|z1|2−|z2|2)).\mathbb{C}^{2}\rightarrow\mathbb{C}\oplus\mathbb{R}\simeq\mathbb{R}^{3};\ (z_{1},z_{2})\mapsto(z_{1}z_{2},\frac{1}{2}(|z_{1}|^{2}-|z_{2}|^{2})).

and the projection map

ℂ⊕ℝ→ℝ;(y,z)↦z.\mathbb{C}\oplus\mathbb{R}\rightarrow\mathbb{R};(y,z)\mapsto z.

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