Algebraic cycles and local quantum cohomology
Abstract
We review the Hodge theory of some classic examples from mirror symmetry, with an emphasis on what is intrinsic to the A-model, and on interesting open questions and problems. In particular, we illustrate the construction of a quantum Z-local system on the cohomology of the total space of the canonical bundle of P2, and suggest how this should be related to the higher algebraic cycles studied in our 2011 CNTP article "Algebraic K-theory of toric hypersurfaces".
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