Metric SYZ conjecture for certain toric Fano hypersurfaces

We prove the metric version of the SYZ conjecture for a class of Calabi–Yau hypersurfaces inside toric Fano manifolds, by solving a variational problem whose minimizer may be interpreted as a global solution of the real Monge–Ampère equation on certain polytopes. This does not rely on discrete symmetry.

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The author is supported by the Clay Mathematics Institute Research Fellowship.

Received 24 February 2023

Published 30 January 2024