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arXiv · 2507.15096

The essential and Cremona dimensions of a group

Igor Dolgachev
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Abstract

The Cremona dimension of a group $G$ is the minimal $n$ such that $G$ is isomorphic to a subgroup of the Cremona group of birational transformations of an $n$-dimensional rational variety. In this survey article, we give many examples that gives evidence to the conjecture that the Cremona dimension of a finite group over the field of complex numbers is less than or equal to the essential dimension of the group.

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Igor Dolgachev. 2025-07-20. The essential and Cremona dimensions of a group. https://arxiv.org/abs/2507.15096

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