On the order of the automorphism group of foliations

Abstract

Let $\mathcal{F}$ be a holomorphic foliation with ample canonical bundle on a smooth projective surface $X$. We obtain an upper bound on the order of its automorphism group which depends only on $K_{\mathcal{F}}^2$ and $K_{\mathcal{F}}{K}_X$, provided this group is finite. Here, $K_{\mathcal{F}}$ and $K_X$ are the canonical bundles of $\mathcal{F}$ and $X$, respectively.

arXiv comment8 pages

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