Séminaire Lotharingien de Combinatoire, 86B.50 (2022), 12 pp.
Maria Gillespie, Sean T. Griffin and Jake Levinson
Tournaments and Slide Rules for Products of ψ and ω Classes on
M0,n
Abstract.
We give two combinatorial rules for the intersections of ψ and ω classes on the Deligne-Mumford moduli space of stable rational curves with n+3 marked points. The first, via lazy tournaments, describes products of ω classes in dimension 0 using boundary points of the moduli space. We use this rule to give a simple proof that the total degree of Mn+3 in the iterated Kapranov embedding is (2n-1)!!, and we give a bijection with the column-restricted parking functions known to enumerate each multidegree. The second rule, via slides, expresses products of ω or ψ classes in all dimensions as positive, multiplicity-free sums of boundary strata. We show that these strata can moreover be obtained as limits of complete intersections of Mn+3 with explicitly-defined families of hyperplanes.
Received: November 25, 2021.
Accepted: March 4, 2022.
Final version: April 1, 2022.
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