Hurwitz numbers for real polynomials

被引:7
作者
Itenberg, Ilia [1 ,2 ]
Zvonkine, Dimitri [3 ]
机构
[1] Sorbonne Univ, Inst Math Jussieu Paris Rive Gauche, 4 Pl Jussieu, F-75252 Paris 5, France
[2] Ecole Normale Super, Dept Math & Applicat, 45 Rue Ulm, F-75230 Paris 5, France
[3] Univ Versailles, Bat Fermat,45 Ave Etats Unis, F-78000 Versailles, France
关键词
Hurwitz numbers; real polynomials; signed count; real enumerative problems; INVARIANTS;
D O I
10.4171/CMH/440
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We consider the problem of defining and computing real analogs of polynomial Hurwitz numbers, in other words, the problem of counting properly normalized real polynomials with fixed ramification profiles over real branch points. We show that, provided the polynomials are counted with an appropriate sign, their number does not depend on the order of the branch points on the real line. We study generating series for the invariants thus obtained, determine necessary and sufficient conditions for the vanishing and nonvanishing of these generating series, and obtain a logarithmic asymptotic for the invariants as the degree of the polynomials tends to infinity.
引用
收藏
页码:441 / 474
页数:34
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