Random real branched coverings of the projective line

13 Jan 2020 Ancona Michele AGL

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... (read more)

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Categories


  • ALGEBRAIC GEOMETRY
  • PROBABILITY