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Mirror Symmetry, Laurent Inversion and the Classification of $\mathbb{Q}$-Fano Threefolds

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arxiv 2210.07328 v1 pith:6X7EZKWN submitted 2022-10-13 math.AG

classification math.AG
keywords fanolaurentmirrorsymmetryclassificationinversionmathbballows
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abstract

We describe recent progress in a program to understand the classification of three-dimensional Fano varieties with $\mathbb{Q}$-factorial terminal singularities using mirror symmetry. As part of this we give an improved and more conceptual understanding of Laurent inversion, a technique that sometimes allows one to construct a Fano variety $X$ directly from a Laurent polynomial $f$ that corresponds to it under mirror symmetry.

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  1. Birational Transformations and 2d (0,2) Quiver Gauge Theories beyond Toric Fano 3-folds

    hep-th 2025-02 conditional novelty 5.0 of 10

    Mass deformations of 2d (0,2) brane brick models are shown in four explicit examples to implement birational transformations of toric Calabi-Yau 4-folds, including non-reflexive toric diagrams.

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