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<p>We obtain results that relate Donaldson-Futaki type invariants (that is, the numerical invariants used to define <i>K</i>-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 <i>K</i>-stability involving elements of the extended Kähler moduli space, i.e. <i>Z</i>-stability for polarised varieties, appear naturally from considerations of mirror symmetry (as a mirror to classical <i>K</i>-stability).</p>

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Toric mirrors and test configurations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月5日

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  • Jacopo Stoppa

摘要

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 Kähler moduli space, i.e. Z-stability for polarised varieties, appear naturally from considerations of mirror symmetry (as a mirror to classical K-stability).