A quantum splitting principle and an application

TL;DR

This paper introduces a quantum splitting principle in genus 0 Gromov--Witten theory, demonstrating how the Gromov--Witten invariants of a variety can be embedded into those of its projectivized vector bundle, with an application provided.

Contribution

It establishes a new analogy of the splitting principle in genus 0 Gromov--Witten theory and shows how to embed the theory of a variety into that of its projectivization.

Findings

Gromov--Witten theory of a variety can be embedded into the theory of its projectivization.

The paper provides an explicit construction of this embedding.

An application of the quantum splitting principle is demonstrated.

Abstract

We propose an analogy of splitting principle in genus $0$ Gromov--Witten theory. More precisely, we show how the Gromov--Witten theory of a variety $X$ can be embedded into the theory of the projectivization of a vector bundle over $X$. An application is also given.