EFFECTIVE DIVISORS ON Mg AND A COUNTEREXAMPLE TO THE SLOPE CONJECTURE
نویسنده
چکیده
The purpose of this note is to prove two statements on the slopes of effective divisors on the moduli space of stable curves Mg: first that the Harris-Morrison Slope Conjecture fails to hold on M10 and second, that in order to compute the slope of Mg for g ≤ 23, one only has to look at the coefficients of the classes λ and δ0 in the expansion of the relevant divisors. The proofs are based on a general result providing inequalities between the first few coefficients of effective divisors on Mg. We give the technical statements in what follows.
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