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arXiv · 2409.06475

The Structure of Algebraic Families of Birational Transformations

Andriy Regeta·Christian Urech·Immanuel van Santen
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Abstract

We give a description of the algebraic families of birational transformations of an algebraic variety X. As an application, we show that the morphisms to Bir(X) given by algebraic families satisfy a Chevalley type result and a certain fibre-dimension formula. Moreover, we show that the algebraic subgroups of Bir(X) are exactly the closed finite-dimensional subgroups with finitely many components. We also study algebraic families of birational transformations preserving a fibration. This builds on previous work of Blanc-Furter, Hanamura, and Ramanujam.

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Andriy Regeta, Christian Urech, Immanuel van Santen. 2024-09-10. The Structure of Algebraic Families of Birational Transformations. https://arxiv.org/abs/2409.06475

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