Mathematics – Algebraic Geometry
Scientific paper
2007-08-16
Compos. Math. 145 (2009) no. 1, 173-195
Mathematics
Algebraic Geometry
minor corrections to match published version
Scientific paper
We give a rigorous definition of tropical fans (the "local building blocks for tropical varieties") and their morphisms. For such a morphism of tropical fans of the same dimension we show that the number of inverse images (counted with suitable tropical multiplicities) of a point in the target does not depend on the chosen point - a statement that can be viewed as the beginning of a tropical intersection theory. As an application we consider the moduli spaces of rational tropical curves (both abstract and in some R^r) together with the evaluation and forgetful morphisms. Using our results this gives new, easy, and unified proofs of various tropical independence statements, e.g. of the fact that the numbers of rational tropical curves (in any R^r) through given points are independent of the points.
Gathmann Andreas
Kerber Michael
Markwig Hannah
No associations
LandOfFree
Tropical fans and the moduli spaces of tropical curves does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Tropical fans and the moduli spaces of tropical curves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Tropical fans and the moduli spaces of tropical curves will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-333189