ScalingStacks

Example 3.1 . [002K]

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Example 3.1.

A typical example of large complex structure limit is the Fermat family of Calabi-Yau hypersurfaces

Xt={Z0Z1…Zn+1+t∑0n+1Zin+2=0}⊂ℂℙn+1.X_{t}=\{Z_{0}Z_{1}\ldots Z_{n+1}+t\sum_{0}^{n+1}Z_{i}^{n+2}=0\}\subset\mathbb{CP}^{n+1}.

As t→0t\to 0, the algebraic limit is the union of n+2n+2 projective planes. Intuitively, the central fibre is highly reducible, and the degeneration is very severe.

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