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Universal Families of Rational Tropical Curves

Published online by Cambridge University Press:  20 November 2018

Georges Francois
Affiliation:
Fachbereich Mathematik, Technische Universität Kaiserslautern, Postfach 3049, 67653 Kaiserslautern, Germany, e-mail: [email protected], e-mail: [email protected]
Simon Hampe
Affiliation:
Fachbereich Mathematik, Technische Universität Kaiserslautern, Postfach 3049, 67653 Kaiserslautern, Germany, e-mail: [email protected], e-mail: [email protected]
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Abstract

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We introduce the notion of families of $n$-marked, smooth, rational tropical curves over smooth tropical varieties and establish a one-to-one correspondence between (equivalence classes of) these families and morphisms from smooth tropical varieties into the moduli space of $n$-marked, abstract, rational, tropical curves ${{\mathcal{M}}_{n}}$.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2013

References

[1] Allermann, L. and Rau, J., First steps in tropical intersection theory. Math. Z. 264(2010), no. 3, 633670. http://dx.doi.org/10.1007/s00209-009-0483-1 http://dx.doi.org/10.1007/s00209-009-0483-1 Google Scholar
[2] Ardila, F. and Klivans, C. J., The Bergman complex of a matroid and phylogenetic trees. J. Combin. Theory, Ser. B 96(2006), no. 1, 3849. http://dx.doi.org/10.1016/j.jctb.2005.06.004 http://dx.doi.org/10.1016/j.jctb.2005.06.004 Google Scholar
[3] François, G., Cocycles on tropical varieties via piecewise polynomials. arxiv:1102.4783v2.Google Scholar
[4] François, G. and Rau, J. , The diagonal of tropical matroid varieties and cycle intersections. arxiv:1012.3260v1.Google Scholar
[5] Feichtner, E. M. andSturmfels, B., Matroid polytopes, nested sets and Bergman fans. Port. Math. (N.S.) 62(2005), no. 4, 437468.Google Scholar
[6] Gathmann, A., Kerber, M., and Markwig, H., Tropical fans and the moduli spaces of tropical curves. Compos. Math. 145(2009), no. 1, 173195. http://dx.doi.org/10.1112/S0010437X08003837 http://dx.doi.org/10.1112/S0010437X08003837 Google Scholar
[7] Kapranov, M. M., Chow quotients of Grassmannians. I. In: I. M. Gel’fand seminar, Adv. Soviet Math., 16, Part 2, American Mathematical Society, Providence, RI, 1993, pp.29110.Google Scholar
[8] Kerber, M. and Markwig, H., Intersecting Psi-classes on tropical M0,n. Int. Math. Res. Not. IMRN 2009(2009), no. 2, 221240.Google Scholar
[9] Kock, J. and Vainsencher, I., An invitation to quantum cohomology. Kontsevich's formula for rational plane curves. Progress in Mathematics, 249, Birkhäuser Boston, Boston, MA, 2007.Google Scholar
[10] G. Mikhalkin, , Tropical geometry and its applications. In: International Congress of Mathematicians, II, Eur. Math. Soc., Zürich, 2006, pp. 827852.Google Scholar
[11] Rau, J., Tropical intersection theory and gravitational descendants. PhD thesis, Technische Universität Kaiserslautern, 2009. http://kluedo.ub.uni-kl.de/volltexte/2009/2370/. Google Scholar
[12] K. M. Shaw, A tropical intersection product in matroidal fans. arxiv:1010.3967v1.Google Scholar
[13] Speyer, D. E., Tropical linear spaces. SIAM J. Discrete Math. 22(2008), no. 4, 15271558. http://dx.doi.org/10.1137/080716219 http://dx.doi.org/10.1137/080716219 Google Scholar
[14]Speyer, D. and Sturmfels, B., The tropical Grassmannian. Adv. Geom. 4(2004), no. 3, 389411. http://dx.doi.org/10.1515/advg.2004.023 http://dx.doi.org/10.1515/advg.2004.023 Google Scholar
[15] Sturmfels, B., Solving systems of polynomial equations. CBMS Regional Conferences Series in Mathematics, 97,Published for the Conference Board of the Mathematical Sciences,Washington, DC; by the American Mathematical Society, Providence, RI, 2002.Google Scholar
[16] Tevelev, J., Compactifications of subvarieties of tori. Amer. J. Math. 129(2007), no. 4, 10871104. http://dx.doi.org/10.1353/ajm.2007.0029 http://dx.doi.org/10.1353/ajm.2007.0029 Google Scholar