TY - JOUR

T1 - RANDOM REAL BRANCHED COVERINGS of the PROJECTIVE LINE

AU - Ancona, Michele

N1 - Publisher Copyright:
©

PY - 2022/9/9

Y1 - 2022/9/9

N2 - 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.

AB - 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.

KW - Bergman kernel

KW - branched coverings

KW - random maps

KW - real algebraic curves

UR - http://www.scopus.com/inward/record.url?scp=85100796164&partnerID=8YFLogxK

U2 - 10.1017/S1474748020000742

DO - 10.1017/S1474748020000742

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AN - SCOPUS:85100796164

SN - 1474-7480

VL - 21

SP - 1783

EP - 1799

JO - Journal of the Institute of Mathematics of Jussieu

JF - Journal of the Institute of Mathematics of Jussieu

IS - 5

ER -