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<p>We generalize the Hodge version of the global Torelli theorem in the framework of irreducible symplectic orbifolds. We also propose a generalization of several results related to the Kähler cone and the notion of wall divisors introduced in the smooth case by Mongardi in (Asian J Math 19(4):583–592, 2015). As an application we propose a definition of the mirror symmetry as an involution on a moduli space; this construction is also new in the smooth case.</p>

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On the Kähler cone of irreducible symplectic orbifolds

  • 期刊论文

  • 发表日期：

    2025年6月6日

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  • Grégoire Menet,
  • Ulrike Riess

摘要

We generalize the Hodge version of the global Torelli theorem in the framework of irreducible symplectic orbifolds. We also propose a generalization of several results related to the Kähler cone and the notion of wall divisors introduced in the smooth case by Mongardi in (Asian J Math 19(4):583–592, 2015). As an application we propose a definition of the mirror symmetry as an involution on a moduli space; this construction is also new in the smooth case.