RANDOM REAL BRANCHED COVERINGS of the PROJECTIVE LINE

Michele Ancona*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we construct a natural probability measure on the space of real branched coverings from a real projective algebraic curve to the projective line. (CP1M, con)We prove that the space of degree d real branched coverings having many real branched points (for example, more than, Formula presented for any α > 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.

Original languageEnglish
Pages (from-to)1783-1799
Number of pages17
JournalJournal of the Institute of Mathematics of Jussieu
Volume21
Issue number5
DOIs
StatePublished - 9 Sep 2022

Keywords

  • Bergman kernel
  • branched coverings
  • random maps
  • real algebraic curves

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