The class of a Hurwitz divisor on the moduli of curves of even genus

Details The class of a Hurwitz divisor on the moduli of curves of even genus The class of a Hurwitz divisor on the moduli of curves of even genus

2010-05-06

arxiv.org/abs/1005.0969v2

Mathematics

Algebraic Geometry

19 pages

Scientific paper

We calculate the cycle class of the Hurwitz divisor $D_2$ on the moduli space of stable curves of genus $g=2k$ given by the degree $k+1$ covers of the projective line with simple ramification points, two of which lie in the same fibre. We also study some aspects of the geometry of the natural map of the Hurwitz space of admissible covers of degree $k+1$ and genus $2k$ to the moduli space of stable curves of genus $2k$.

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