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<p>We define 2-categories of microlocal perverse (resp. coherent) sheaves of categories on the skeleton of a hypertoric variety and show that the generators of these 2-categories lift the projectives (resp. simples) in hypertoric category <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\({\mathcal {O}}.\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">O</mi> <mo>.</mo> </mrow> </math></EquationSource> </InlineEquation> We then establish equivalences of 2-categories categorifying the Koszul duality between Gale dual hypertoric categories <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\({\mathcal {O}}.\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">O</mi> <mo>.</mo> </mrow> </math></EquationSource> </InlineEquation> These constructions give a prototype for understanding symplectic duality via the fully extended 3d mirror symmetry conjecture.</p>

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Hypertoric 2-Categories \(\mathcal {O}\) and Symplectic Duality

  • 期刊论文

  • 发表日期：

    2026年2月5日

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  • Benjamin Gammage,
  • Justin Hilburn

摘要

We define 2-categories of microlocal perverse (resp. coherent) sheaves of categories on the skeleton of a hypertoric variety and show that the generators of these 2-categories lift the projectives (resp. simples) in hypertoric category \({\mathcal {O}}.\) O . We then establish equivalences of 2-categories categorifying the Koszul duality between Gale dual hypertoric categories \({\mathcal {O}}.\) O . These constructions give a prototype for understanding symplectic duality via the fully extended 3d mirror symmetry conjecture.