Divisors on the Moduli Space of Curves From Divisorial Conditions On Hypersurfaces

In this note, we extend work of Farkas and Rimányi on applying quadric rank loci to finding divisors small slope the moduli space curves by instead considering all divisorial conditions hypersurfaces a fixed degree containing projective curve. This gives rise large family virtual Mg¯. We determine explicitly which these are candidate counterexamples Slope Conjecture. The potential exist Mg¯, where set possible values g∈{1,…,N} has density Ω( log (N)−0.087) for N≫0. Furthermore, no condition defined using greater than 2 give Conjecture, every divisor in our at least 6+8g+1.