Moduli spaces of rational tropical curves

By G. Mikhalkin. 2007

122 citations recorded by the source corpus.

This note is devoted to the definition of moduli spaces of rational tropical curves with n marked points. We show that this space has a structure of a smooth tropical variety of dimension n-3. We define the Deligne-Mumford compactification of this space and tropical $\psi$-class divisors.

Subfields: Algebra and Number Theory, Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/d5e2972a7f1636a8c372248b7b1564924212b18d

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In Algebra and Number Theory

1. Melody Chan
2. Erwan Brugallé
3. Lucia Caporaso
4. I. Itenberg
5. Kristin M. Shaw
6. Hannah Markwig
7. Filippo Viviani
8. Renzo Cavalieri

In Computational Mechanics

1. I. Itenberg
2. Lucia Caporaso
3. Melody Chan
4. Hannah Markwig
5. Erwan Brugallé
6. Renzo Cavalieri
7. Silvia Brannetti
8. Margarida Melo

In Computational Theory and Mathematics

1. Melody Chan
2. Lucia Caporaso
3. Erwan Brugallé
4. I. Itenberg
5. Kristin M. Shaw
6. G. Mikhalkin
7. Filippo Viviani
8. Hannah Markwig

Citations in the corpus

• On the tropical Torelli map (2009, background): “Though, the moduli space of n-pointed tropical rational curves M tr 0,n was constructed by different authors (see [56, 42,23,30]).”
• Tropical Hurwitz numbers (2008, background): “-marked abstract tropical curves is a tropical fan - it is just the space of trees, respectively, the tropical Grassmanian modulo the homogeneity space, see [SS04].) The following definition is due to [Mik07]. Definition 9.3 (Psi-class) For k∈ {1,...,N}, the tropical Psi-class Ψk ⊂ M0,N is the union o”
• Algebraic and tropical curves: comparing their moduli spaces (2011, background): “A detailed description of the case g = 0 and n ≥ 4, with nice pictures, can be found in [23].”
• Brief introduction to tropical geometry (2015, background): “This tropical space is also the moduli space of 5-marked tropical rational curves (see [Mik07]).”
• Tropical intersection theory from toric varieties (2009, unknown): “Mikhalkin introduced a tropical ψ-class in [15].”
• Combinatorics of the tropical Torelli map (2010, background): “” Contrast this with the situation of moduli space M0,n of tropical rational curves with n marked points, constructed and studied in [Speyer and Sturmfels 2004; Mikhalkin 2007; Gathmann et al. 2009].”