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 -