Cambridge Journal of Mathematics

Volume 12 (2024)

Number 1

Metric SYZ conjecture for certain toric Fano hypersurfaces

Pages: 223 – 252

DOI: https://dx.doi.org/10.4310/CJM.2024.v12.n1.a3

Author

Yang Li (Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Mass., U.S.A.)

Abstract

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