Geodesic
Irreducible cycles and points in special position in moduli spaces for tropical curves
Andreas Gathmann1 ; Franziska Schroeter2
1Fachbereich Mathematik TU Kaiserslautern Postfach 3049, 67653 Kaiserslautern, Germany
2Cluster of Excellence for Computer Science Universität des Saarlandes Postfach 151150, 66041 Saarbrücken, Germany
The electronic journal of combinatorics, Tome 19 (2012) no. 4
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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.
DOI : 10.37236/2862
Classification : 14N10
Mots-clés : tropical cycles, tropical curves, general position, irreducibility

Andreas Gathmann  1   ; Franziska Schroeter  2

1 Fachbereich Mathematik TU Kaiserslautern Postfach 3049, 67653 Kaiserslautern, Germany
2 Cluster of Excellence for Computer Science Universität des Saarlandes Postfach 151150, 66041 Saarbrücken, Germany 
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     author = {Andreas Gathmann and Franziska Schroeter},
     title = {Irreducible cycles and points in special position in moduli spaces for tropical curves},
     journal = {The electronic journal of combinatorics},
     year = {2012},
     volume = {19},
     number = {4},
     doi = {10.37236/2862},
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     url = {http://geodesic.mathdoc.fr/articles/10.37236/2862/}
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Andreas Gathmann; Franziska Schroeter. Irreducible cycles and points in special position in moduli spaces for tropical curves. The electronic journal of combinatorics, Tome 19 (2012) no. 4. doi: 10.37236/2862

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