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

الأصل · EN

We calculate the cycle class of the Hurwitz divisor D₂ 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.