Scattering Diagrams, Sheaves, and Curves

  title={Scattering Diagrams, Sheaves, and Curves},
  author={Pierrick Bousseau},
  journal={Acta Mathematica Sinica, English Series},
  • Pierrick Bousseau
  • Published 20 February 2020
  • Mathematics
  • Acta Mathematica Sinica, English Series
We review the recent proof of the N.Takahashi's conjecture on genus $0$ Gromov-Witten invariants of $(\mathbb{P}^2, E)$, where $E$ is a smooth cubic curve in the complex projective plane $\mathbb{P}^2$. The main idea is the use of the algebraic notion of scattering diagram as a bridge between the world of Gromov-Witten invariants of $(\mathbb{P}^2, E)$ and the world of moduli spaces of coherent sheaves on $\mathbb{P}^2$. Using this bridge, the N.Takahashi's conjecture can be translated into a… 



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