ScalingStacks

Assumption 8.1 [03MF]

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Assumption 8.1 Let ℤ\mathbin{\mathbb{Z}} act on ℂ3\mathbin{\mathbb{C}}^{3} by (z1,z2,z3)↦n(z1,z2,z3+2​π​n)(z_{1},z_{2},z_{3})\,{\mathrel{\mathop{\kern 0.0pt\mapsto}\limits^{n}}}\,(z_{1},z_{2},z_{3}+2\pi n) for n∈ℤn\in\mathbin{\mathbb{Z}}. Define U={(z1,z2,z3+2πℤ)∈ℂ3/ℤ:Im(z1z2)∈[−π,π]}U=\bigl\{(z_{1},z_{2},z_{3}\!+\!2\pi\mathbin{\mathbb{Z}})\in\mathbin{\mathbb{C}}^{3}/\mathbin{\mathbb{Z}}:\mathop{\rm Im}(z_{1}z_{2})\in[-\pi,\pi]\bigr\}. Consider a special Lagrangian fibration f:U→ℝ3f:U\rightarrow\mathbin{\mathbb{R}}^{3}, with fibres Na,b,c=f−1​(a,b,c)N_{a,b,c}=f^{-1}(a,b,c). Suppose that ff satisfies parts (i)–(viii) of Assumption 7.1.

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