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Global shifted potentials for moduli spaces of sheaves on CY4

Research output: Working paper/Preprint Working paperResearch



  • Dennis Borisov, Harvard University
  • ,
  • Artan Sheshmani, Higher School of Economics, Harvard University
  • ,
  • Shing-Tung Yau, Harvard University, United States
It is shown that any derived scheme over $\mathbb C$ equipped with a $-2$-shifted symplectic structure, and having a Hausdorff space of classical points, admits a globally defined Lagrangian distribution as a dg $\mathbb{C}^{\infty}$-manifold. The main tool for proving this theorem is a strictification result for Lagrangian distribution. It is shown that existence of a global Lagrangian distribution allows us to realize the moduli space of sheaves on Calabi-Yau fourfolds as a derived critical locus of a potential of degree $-1$ on the moduli space of $Spin(7)$ instantons.
Original languageEnglish
Publication statusPublished - 1 Aug 2019

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