Aarhus Universitets segl

Global shifted potentials for moduli spaces of sheaves on CY4

Publikation: Working paper/Preprint Working paperForskning


  • 1908.00651v1

    Forlagets udgivne version, 364 KB, PDF-dokument


  • Dennis Borisov, Harvard University
  • ,
  • Artan Sheshmani, Higher School of Economics, Harvard University
  • ,
  • Shing-Tung Yau, Harvard University, USA
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.
StatusUdgivet - 1 aug. 2019


  • math.AG, hep-th, math.DG

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