BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Tropicalizing cycle classes and a correspondence theorem for descendant invariants Gross, Andreas


Intersection theory is an extremely useful tool both in algebraic and tropical enumerative geometry. It can also be used to obtain algebraic/tropical correspondence theorems. The idea is to apply the tropicalization procedure to appropriate intersection products on suitable algebraic moduli spaces, thus obtaining the analogous tropical intersection products on the analogous tropical moduli spaces. For this to work in general, we need to be able to tropicalize cycle classes. I will present a suitable definition of tropical rational equivalence on extended cone complexes making this possible. As an application we obtain a correspondence theorem for genus 0 logarithmic descendant Gromov-Witten invariants of toric varieties.

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