Filtrations of moduli spaces of tropical weighted stable curves

2021/11/29 by Serpente, Stefano
#Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2111.14965

Abstract

We study how changing the weight datum A=(a₁,...,a_n)∈(ℚ∩(0,1])ⁿ affects the topology of tropical moduli spaces M_g,A^trop, M_g,A^trop and Δ_g,A and the homology of the latter one. We show that for fixed g and n, there are particular filtrations of these topological spaces which we can use to compute the reduced rational homology of Δ_g,A and the top weight cohomology of the moduli space M_g,A of smooth (g,A)-stable algebraic curves.

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