A geometric interpretation and a new proof of a relation by Cornalba and Harris

Details A geometric interpretation and a new proof of a relation by Cornalba and Harris A geometric interpretation and a new proof of a relation by Cornalba and Harris

2000-08-22

arxiv.org/abs/math/0008176v1

Mathematics

Algebraic Geometry

12 pages, LaTeX file

Scientific paper

In the 80's M. Cornalba and J. Harris discovered a relation among the Hodge class and the boundary classes in the Picard group with rational coefficients of the moduli space of stable, hyperelliptic curves. They proved the relation by computing degrees of the classes involved for suitable one-parameter families. In the present article we show that their relation can be obtained as the class of an appropriate, geometrically meaningful empty set, thus conforming with C. Faber's general philosophy to finding relations among tautological classes in the Chow ring of the moduli space of curves. The empty set we consider is the closure of the locus of smooth, hyperelliptic curves having a special ramification point.

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