Realization spaces for tropical fans

Details Realization spaces for tropical fans Realization spaces for tropical fans

2009-09-25

arxiv.org/abs/0909.4582v2

Combinatorial aspects of commutative algebra and algebraic geometry, Abel Symp., 6, Springer 2011, 73--88

Mathematics

Algebraic Geometry

14 pages. v2: minor expository changes, updated references. To appear in Proceedings of the Abel Symposium

Scientific paper

We introduce a moduli functor for varieties whose tropicalization realizes a given weighted fan and show that this functor is an algebraic space in general, and is represented by a scheme of finite type when the associated toric variety is quasiprojective. We study the geometry of these tropical realization spaces for the matroid fans studied by Ardila and Klivans, and show that the tropical realization space of a matroid fan is a torus torsor over the realization space of the matroid. As a consequence, we deduce that these tropical realization spaces satisfy Murphy's Law.

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