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On the relative cone conjecture for families of IHS manifolds

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arxiv 2410.11987 v1 pith:VD77DGGV submitted 2024-10-15 math.AG

Andreas Höring , Gianluca Pacienza , Zhixin Xie This is my paper · ORCID
classification math.AG
keywords relativeconeconjecturefamiliesmanifoldsapplicationconjecturesdeformation
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abstract

We study the relative cone conjecture for families of $K$-trivial varieties with vanishing irregularity. As an application we prove that the relative movable and the relative nef cone conjectures hold for fibrations in projective IHS manifolds of the 4 known deformation types.

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  1. On the Morrison-Kawamata dream space and its applications

    math.AG 2025-12 conditional novelty 7.0 of 10

    An axiomatic framework (MKD spaces) yields deformation-invariance of divisor cones and a conditional boundedness theorem for rationally connected Calabi–Yau varieties.

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