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Group actions and irrationality in surface families

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arxiv 2410.18427 v1 pith:OG2AMI7N submitted 2024-10-24 math.AG

Nathan Chen , Louis Esser This is my paper · ORCID
classification math.AG
keywords irrationalitydegreefamiliesgroupactionactionsanalogousarises
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Rationality specializes in families of surfaces, even with mild singularities. In this paper, we study the analogous question for the degree of irrationality. We prove a specialization result when the degree of irrationality on the generic fiber arises from the quotient by a group action.

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  1. A primer on measures of irrationality

    math.AG 2025-09 conditional

    An expository survey of degree of irrationality, covering gonality, and related invariants, organized by the Kodaira-Enriques classification, with many open problems.

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