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${\mathbb {Q}}$-FANO THREEFOLDS AND LAURENT INVERSION
Published online by Cambridge University Press: 20 January 2025
Abstract
We construct families of non-toric ${\mathbb {Q}}$-factorial terminal Fano (
${\mathbb {Q}}$-Fano) threefolds of codimension
$\geq 20$ corresponding to 54 mutation classes of rigid maximally mutable Laurent polynomials. From the point of view of mirror symmetry, they are the highest codimension (non-toric)
${\mathbb {Q}}$-Fano varieties for which we can currently establish the Fano/Landau–Ginzburg correspondence. We construct 46 additional
${\mathbb {Q}}$-Fano threefolds with codimensions of new examples ranging between 19 and 5. Some of these varieties are presented as toric complete intersections, and others as Pfaffian varieties.
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- © The Author(s), 2025. Published by Cambridge University Press on behalf of Foundation Nagoya Mathematical Journal
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