# The Log Product Formula

## TL;DR

This paper proves a formula relating Log Gromov-Witten Invariants of product varieties to those of the factors, extending previous results using advanced log geometry tools.

## Contribution

It introduces a new formula for Log Gromov-Witten invariants of product varieties, expanding the theoretical framework in log geometry.

## Key findings

- Established a product formula for Log Gromov-Witten invariants
- Extended previous results by F. Qu and Y.P. Lee
- Developed new notions of log normal cone and log virtual fundamental class

## Abstract

We prove a formula expressing the Log Gromov-Witten Invariants of a product of log smooth varieties $V \times W$ in terms of the invariants of $V$ and $W$. This extends results of F. Qu and Y.P. Lee, who introduced this formula analogously to K. Behrend. The proof requires notions of "log normal cone" and "log virtual fundamental class," as well as modified versions of standard intersection-theoretic machinery adapted to Log Geometry.