Corpus ID: 17859206

Calabi-Yau algebras

  title={Calabi-Yau algebras},
  author={V. Ginzburg},
  journal={arXiv: Algebraic Geometry},
  • V. Ginzburg
  • Published 2006
  • Mathematics, Physics
  • arXiv: Algebraic Geometry
We introduce some new algebraic structures arising naturally in the geometry of Calabi-Yau manifolds and mirror symmetry. We give a universal construction of Calabi-Yau algebras in terms of a noncommutative symplectic DG algebra resolution. In dimension 3, the resolution is determined by a noncommutative potential. Representation varieties of the Calabi-Yau algebra are intimately related to the set of critical points, and to the sheaf of vanishing cycles of the potential. Numerical invariants… Expand
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