Communications in Number Theory and Physics

Volume 8 (2014)

Number 4

Algebraic cycles and local quantum cohomology

Pages: 703 – 727



Charles F. Doran (Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada)

Matt Kerr (Department of Mathematics, Washington University, St. Louis, Missouri, U.S.A.)


We review the Hodge theory of some classic examples from mirror symmetry, with an emphasis on what is intrinsic to the A-model. In particular, we illustrate the construction of a quantum $\mathbb{Z}$-local system on the cohomology of $K_{\mathbb{P}^2}$ and suggest how this should be related to the higher algebraic cycles studied in [10].

Published 24 February 2015