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Super J -holomorphic curves: construction of the moduli space

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  • Enno Keßler, Harvard University
  • ,
  • Artan Sheshmani, Harvard University, Higher School of Economics
  • ,
  • Shing Tung Yau, Harvard University

Let M be a super Riemann surface with holomorphic distribution D and N a symplectic manifold with compatible almost complex structure J. We call a map Φ : M→ N a super J-holomorphic curve if its differential maps the almost complex structure on D to J. Such a super J-holomorphic curve is a critical point for the superconformal action and satisfies a super differential equation of first order. Using component fields of this super differential equation and a transversality argument we construct the moduli space of super J-holomorphic curves as a smooth subsupermanifold of the space of maps M→ N.

TidsskriftMathematische Annalen
Sider (fra-til)1391-1449
Antal sider59
StatusUdgivet - aug. 2022

Bibliografisk note

Funding Information:
Enno Keßler was supported by a Deutsche Forschungsgemeinschaft Research Fellowship, KE2324/1–1. Artan Sheshmani was supported partially by the NSF DMS-1607871, NSF PHY-1306313, the Simons 38558, and Laboratory of Mirror Symmetry NRU HSE, RF Government grant, ag. No 14.641.31.0001. Shing-Tung Yau was partially supported by NSF DMS-1607871, NSF PHY-1306313, and Simons 38558. We thank Vladimir Baranovsky, Christopher Beasley, Roman Bezrukavnikov, Dennis Borisov, Ron Donagi, Jürgen Jost, Valentino Tosatti and Ruijun Wu for useful discussion and comments. The second author would like to thank Professors Yuri Manin, Sheldon Katz, Michael Kapranov, Ron Donagi and Tony Pantev who advised him about the notions of supergeometry in the past years.

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

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