I will explain the construction of a continuous and functorial tropicalization map on the moduli space of logarithmic stable maps to a logarithmically smooth scheme. The basic fuel for this construction is the perfect obstruction theory that gives rise to the virtual fundamental class in logarithmic Gromov-Witten theory. Specializing to the case of toric varieties, this framework gives simple conceptual proofs of several fundamental correspondence principles in tropical geometry. I will explain a tropical version of Vakil's Murphy's Law, which states that the question of which tropical curves are realizable by stable maps to toric varieties is, in general, arbitrarily difficult to answer.
Math-Physics Joint Seminar
Thursday, March 31, 2016 - 4:30pm
Dhruv Ranganathan
Yale University