Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

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.
Complete list of metadatas

Cited literature [14 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02434851
Contributor : Michele Ancona <>
Submitted on : Friday, January 10, 2020 - 1:33:39 PM
Last modification on : Tuesday, January 21, 2020 - 2:24:35 PM
Document(s) archivé(s) le : Saturday, April 11, 2020 - 5:30:12 PM

Files

RealBranched.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-02434851, version 1
  • ARXIV : 2001.04220

Citation

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

Share

Metrics

Record views

60

Files downloads

20