# The extended tropical vertex group.

@article{Fantini2020TheET, title={The extended tropical vertex group.}, author={Veronica Fantini}, journal={arXiv: Algebraic Geometry}, year={2020} }

In this thesis we study the relation between scattering diagrams and deformations of holomorphic pairs, building on a recent work of Chan--Conan Leung--Ma. The new feature is the extended tropical vertex group where the scattering diagrams are defined. In addition, the extended tropical vertex provides interesting applications: on one hand we get a geometric interpretation of the wall-crossing formulas for coupled $2d$-$4d$ systems, previously introduced by Gaiotto--Moore--Neitzke. On the other…

## 2 Citations

### INFINITESIMAL DEFORMATIONS AND THE EXTENDED TROPICAL VERTEX GROUP

- Mathematics
- 2022

I will discuss the relationship between scattering diagrams and infinitesimal deformations of holomorphic pairs, which Fukaya outlined in [4], and which I studied in my PhD thesis [3]. Scattering…

### Scattering diagrams in mirror symmetry

- Physics
- 2023

Since the pioneering work of Kontsevich and Soibelman [33], scattering diagrams have started playing an important role in mirror symmetry, in particular the study of the reconstructing problem. This…

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