RANDOM REAL BRANCHED COVERINGS OF THE PROJECTIVE LINE

被引：0

作者：

Ancona, Michele ^{[1
]}

机构：

[1] Tel Aviv Univ, Sch Math Sci, Tel Aviv, Israel

来源：

JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU | 2022年 / 21卷 / 05期

关键词：

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

D O I：

10.1017/S1474748020000742

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 (CP1, conj). We prove that the space of degree d real branched coverings having "many" real branched points (for example, more than root 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.

引用

页码：1783 / 1799

页数：17

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