# Variations on the theme of quantum Lefschetz

## TL;DR

This paper explores variations of quantum Lefschetz formulas, reformulating recursions via Givental's formalism and auxiliary space modifications, leading to new relations in Gromov--Witten invariants.

## Contribution

It introduces new reformulations of quantum Lefschetz recursions and explores auxiliary space modifications, expanding the toolkit for Gromov--Witten theory.

## Key findings

- Reformulation of quantum Lefschetz recursions using Givental's quantization.
- Introduction of modified auxiliary spaces for fixed point localization.
- Derivation of new relations among Gromov--Witten invariants.

## Abstract

In this companion piece to 1712.03573, some variations on the main results there are sketched. In particular, the recursions in 1712.03573, which we interpreted as the quantum Lefschetz, is reformulated in terms of Givental's quantization formalism, or equivalently, a summation of finitely many graphs. Meanwhile, varieties of modification of the auxilliary spaces (masterspaces) for the fixed point localization are given, leading to different (looking) recursions. There are also some applications of this circle of ideas to derive (apparently) new relations of Gromov--Witten invariants.