论文标题
投影线的随机真实分支覆盖物
Random real branched coverings of the projective line
论文作者
论文摘要
在本文中，我们从真实的分支覆盖物的空间中构建了一种自然概率度量，从真实的投影代数曲线$（x，c_x）$到投影线$（\ Mathbb {c} \ Mathbb {p}^1，\ textrm {conj}）$。我们证明，对于任何$α> 0 $），学位的空间$ d $真实的分支覆盖物具有“许多”真实的分支点（例如，超过$ \ sqrt {d}^{1+α} $，其指数呈小尺寸。特别是，最大的真实分支覆盖物，即真实的分支覆盖物，使所有分支点都是真实的，是指数千的。
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 $\sqrt{d}^{1+α}$, 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.
