Upper bounds for logarithmic Gromov-Witten invariants of projective space

TL;DR

This paper establishes polynomial upper bounds for genus zero logarithmic Gromov-Witten invariants of projective space relative to its toric boundary, based on intersection positivity.

Contribution

It introduces a new polynomial upper bound for these invariants, linking their growth to contact orders and marked points.

Findings

Upper bounds are polynomial in contact orders.

Degree of bounds depends on the number of marked points.

Positivity of intersections is key to the proof.

Abstract

We provide an upper bound for the genus zero logarithmic Gromov-Witten invariants of projective space relative to its toric boundary. The upper bound is polynomial in the contact orders, with degree depending on the number of marked points. The result hinges on the positivity of intersections for projective spaces.