Corpus ID: 119748019

Generating the Fukaya categories of compact toric varieties

  title={Generating the Fukaya categories of compact toric varieties},
  author={Jack Smith},
  • Jack Smith
  • Published 2018
  • Mathematics
  • Let $X$ be a compact toric variety. The quantum cohomology of $X$ decomposes as a direct sum, and associated to each summand $Q$ is a toric fibre $L_Q$ with rank $1$ local system. By building an explicit twisted-complex-like object, we show that on $Q$ the Kodaira-Spencer isomorphism of Fukaya-Oh-Ohta-Ono factors through the closed-open string map to the Hochschild cohomology of $L_Q$. We deduce that the latter is injective and hence, assuming an appropriate version of Abouzaid's criterion… CONTINUE READING

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