Quantum Periods for Certain Four-Dimensional Fano Manifolds

ABSTRACT

We collect a list of known four-dimensional Fano manifolds and compute their quantum periods. This list includes all four-dimensional Fano manifolds of index greater than one, all four-dimensional toric Fano manifolds, all four-dimensional products of lower-dimensional Fano manifolds, and certain complete intersections in projective bundles.

KEYWORDS:

• Fano manifolds
• $\text{four}$-folds
• mirror symmetry
• quantum period

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 14J45, 14N35
• Secondary 14J33

Notes

1 The proof of extremality involves applying the generalized Griffiths–Dwork algorithm of Lairez [Lairez 16] to f.

Additional information

Funding

This research was supported by a Royal Society University Research Fellowship (TC); ERC Starting Investigator Grant number 240123; the Leverhulme Trust; grant MK-1297.2014.1; AG Laboratory NRU-HSE, RF government grant ag. 11.G34.31.0023; Grant of Leading Scientific Schools (N.Sh. 2998.2014.1); EPSRC grant EP/I008128/1, and EPSRC Fellowship EP/N022513/1.