Rational correspondences between moduli spaces of curves defined by Hurwitz spaces

Mathematics – Algebraic Geometry

Scientific paper

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25 pages, latex

Scientific paper

By associating to a curve C of genus g=2k and a pencil of degree d=k+1 the
so-called trace curve (resp. the reduced trace curve) we define a rational map
from the Hurwitz space of admissible covers of genus g=2k and degree d=k+1 to a
moduli space of stable curves. We study the induced map between the divisor
class groups of these moduli spaces of curves.

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