Random real branched coverings of the projective line

Michele Ancona 1
1 AGL - Algèbre, géométrie, logique
ICJ - Institut Camille Jordan [Villeurbanne]
Abstract : In this paper, we construct a natural probability measure on the space of real branched coverings from a real projective algebraic curve $(X,c_X)$ to the projective line $(\mathbb{C}\mathbb{P}^1,\textrm{conj})$. We prove that the space of degree $d$ real branched coverings having "many" real branched points (for example more than $\sqrt{d}^{1+\alpha}$, for any $\alpha>0$) has exponentially small measure. In particular, maximal real branched coverings, that is real branched coverings such that all the branched points are real, are exponentially rare.
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Submitted on : Friday, January 10, 2020 - 1:33:39 PM
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  • HAL Id : hal-02434851, version 1
  • ARXIV : 2001.04220

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Michele Ancona. Random real branched coverings of the projective line. 2020. ⟨hal-02434851⟩

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