Irreducible Cycles and Points in Special Position in Moduli Spaces for Tropical Curves

  • Andreas Gathmann
  • Franziska Schroeter
Keywords: Tropical geometry


In the first part of this paper, we discuss the notion of irreducibility of cycles in the moduli spaces of $n$-marked rational tropical curves. We prove that Psi-classes and vital divisors are irreducible, and that locally irreducible divisors are also globally irreducible for $ n \le 6 $. In the second part of the paper, we show that the locus of point configurations in $({\mathbb R}^2)^n $ in special position for counting rational plane curves (defined in two different ways) can be given the structure a tropical cycle of codimension $1$. In addition, we compute explicitly the weights of this cycle.
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