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arXiv · 2512.02837

Characterizing Varieties Using Birational Transformations

Nathan Chen·Louis Esser·Andriy Regeta·Christian Urech·Immanuel van Santen
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Abstract

Suppose $X$ is an irreducible complex variety. We show that when $X$ is ruled, the group of birational transformations $Bir(X)$, as a group, determines $X$ up to birational transformations and automorphisms of the base field. In contrast, we demonstrate that this same property never holds for non-uniruled varieties.

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Nathan Chen, Louis Esser, Andriy Regeta, Christian Urech, Immanuel van Santen. 2025-12-02. Characterizing Varieties Using Birational Transformations. https://arxiv.org/abs/2512.02837

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