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arXiv · 2410.05036

Birational invariants of volume preserving maps

Konstantin Loginov·Zhijia Zhang
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Abstract

We study the group of birational automorphisms of the $n$-dimensional projective space that preserve the standard torus invariant volume form with logarithmic poles. We prove that this group is not generated by pseudo-regularizable maps for $n\geq 4$ over $\mathbb{C}$, and for $n\geq 3$ over number fields. As a corollary, we show that this group is not simple in these cases.

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Konstantin Loginov, Zhijia Zhang. 2024-10-07. Birational invariants of volume preserving maps. https://arxiv.org/abs/2410.05036

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