Relative Calabi–Yau structures II: shifted Lagrangians in the moduli of objects

• Christopher Brav ^[1] ; Tobias Dyckerhoff ^[2]
  1. [1] Higher School of Economics, National Research University

     Higher School of Economics, National Research University

     Rusia

     
  2. [2] Universitaet Hamburg, Alemania
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 27, Nº. 4, 2021
• Idioma: inglés
• DOI: 10.1007/s00029-021-00642-5
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• Resumen

  • We show that a Calabi–Yau structure of dimension d on a smooth dg category C induces a symplectic form of degree 2−d on ‘the moduli space of objects’ MC. We show moreover that a relative Calabi–Yau structure on a dg functor C→D compatible with the absolute Calabi–Yau structure on C induces a Lagrangian structure on the corresponding map of moduli MD→MC.