Resumen de Tropical compactification and the Gromov–Witten theory of P1

Renzo Cavalieri, Hannah Markwig, Dhruv Ranganathan

• We use tropical and non-archimedean geometry to study the moduli space of genus 0, stable maps to P1 relative to two points. This space is exhibited as a tropical compactification in a toric variety. Moreover, the fan of this toric variety may be interpreted as a moduli space for tropical relative stable maps with the same discrete data. As a consequence, we confirm an expectation of Bertram and the first two authors, that the tropical Hurwitz cycles are tropicalizations of classical Hurwitz cycles. As a second application, we obtain a full descendant correspondence for genus 0 relative invariants of P1.