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${\mathbb {Q}}$-FANO THREEFOLDS AND LAURENT INVERSION

Part of: Special varieties Surfaces and higher-dimensional varieties

Published online by Cambridge University Press:  20 January 2025

LIANA HEUBERGER Open the ORCID record for LIANA HEUBERGER [Opens in a new window]
LIANA HEUBERGER*
Affiliation:
Institut de Mathématiques de Marseille 3 Place Victor Hugo 13331 Marseille Cedex 3 France
*
liana.heuberger@univ-amu.fr
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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.

Keywords

Fano varietiesmirror symmetrytoric degenerations

MSC classification

Primary: 14J45: Fano varieties 14M25: Toric varieties, Newton polyhedra
Secondary: 14J33: Mirror symmetry
Type
Article
Information
Nagoya Mathematical Journal , First View , pp. 1 - 47
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Foundation Nagoya Mathematical Journal

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