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arXiv · 2412.03189

Toric mirrors and test configurations

Jacopo Stoppa
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Abstract

We obtain results that relate Donaldson-Futaki type invariants (that is, the numerical invariants used to define K-stability for general polarised manifolds) for a toric polarised manifold and for a compactification of its mirror Landau-Ginzburg model, nearby the large volume limit. In general, these have the form of expansions containing terms which involve the base loci of certain linear systems determined by the Landau-Ginzburg potential (as expected from known constructions of compactified mirrors), and we give a condition under which these terms are subleading. As an application we show that recently proposed notions of K-stability involving elements of the extended K\"ahler moduli space, i.e. Z-stability for polarised varieties, appear naturally from considerations of mirror symmetry (as a mirror to classical K-stability).

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Jacopo Stoppa. 2024-12-04. Toric mirrors and test configurations. https://arxiv.org/abs/2412.03189

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