Abstract:

Abstract: One of the major successes of tropical geometry is Mikhalkin's correspondence theorem, which relates complex and tropical curves in toric surfaces. In non-toric surfaces Mikhalkin's correspondence does not hold; there are tropical curves not arising from complex curves or algebraic curves over any field. We will explain some local obstructions to approximating tropical curves coming from a tropical intersection product. This product is related to the intersection product defined by Kaveh and Khovanskii on divisors in more general spaces. We will also see examples of tropical curves which do not satisfy some classical theorems of geometry.