Corpus ID: 201646086

The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus

  title={The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus},
  author={S. Keel and Tony Yue Yu},
  journal={arXiv: Algebraic Geometry},
  • S. Keel, T. Yu
  • Published 26 August 2019
  • Mathematics
  • arXiv: Algebraic Geometry
We show that the naive counts of rational curves in any affine log Calabi-Yau variety $U$, containing an open algebraic torus, determine in a surprisingly simple way, a family of log Calabi-Yau varieties, as the spectrum of a commutative associative algebra equipped with a compatible multilinear form. This is directly inspired by a very similar conjecture of Gross-Hacking-Keel in mirror symmetry, known as the Frobenius structure conjecture. Although the statement involves only elementary… Expand

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