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N\'eron models, minimal models, and birational group actions

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arxiv 2502.13800 v1 pith:SZZ65UEC submitted 2025-02-19 math.AG math.NT

János Kollár This is my paper · ORCID
classification math.AGmath.NT
keywords modeleronminimalactionsbirationalgroupmodelsabelian
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abstract

Let $A_K$ be an Abelian variety over the quotient field of a Dedekind domain $R$. We show that the identity component of the N\'eron model of $A_K$ acts regularly on any minimal model of $A_K$ over $R$, and discuss when the N\'eron model is an open subset of a minimal model. The main technical result is the rigidity of small modifications, leading to a regularity criterion for birational group actions.

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Cited by 3 Pith papers

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    math.AG 2025-07 conditional novelty 8.0 of 10

    Fixed-dimension Calabi-Yau varieties with abelian or primitive symplectic fibrations are birationally bounded, and Lagrangian-fibered primitive symplectic varieties have finitely many deformation classes.

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    math.AG 2025-08 conditional novelty 7.0 of 10

    Flat projective morphisms between characteristic-zero varieties with rational singularities have locally free higher direct images of O_X and of the relative dualizing sheaf, making Pic^0(X/S) smooth.

  3. On the finiteness of log surfaces

    math.AG 2025-10 conditional novelty 4.0 of 10

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