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arXiv · 2606.10207

Galois self-covers of projective spaces and essential dimensions

Yujie Luo·De-Qi Zhang
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Abstract

We give the structure theorem of Galois self-covers $f: \mathbf{P}^n \to \mathbf{P}^n$. As an application, we show that the essential dimension of every such nontrivial cover attains its maximum possible value $n$. As another application, we prove that the pair $(\mathbf{P}^n, R_f/(q-1))$ is log Calabi-Yau as conjectured by Gongyo, where $R_f$ is the ramification divisor and we write $f^*\mathcal{O}(1) = \mathcal{O}(q)$.

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Yujie Luo, De-Qi Zhang. 2026-06-08. Galois self-covers of projective spaces and essential dimensions. https://arxiv.org/abs/2606.10207

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