Counting curves on Hirzebruch surfaces: tropical geometry and the Fock space

We study the stationary descendant Gromov–Witten theory of toric surfaces by combining and extending a range techniques – tropical curves, floor diagrams Fock spaces. A correspondence theorem is established between curves invariants on using maximal degenerations. An intermediate degeneration then shown to give rise diagrams, giving geometric interpretation this well-known bookkeeping tool in geometry. In process, we extend diagram include descendants arbitrary genus. These are used connect curve counting algebra operators bosonic space, showno coincide with Feynman appropriate operators. This extends work number researchers, including Block–Göttsche, Cooper–Pandharipande Block–Gathmann–Markwig.