Algebraic cycles and local quantum cohomology
Charles F. Doran, Matt Kerr
TL;DR
This paper reviews the Hodge theory in mirror symmetry, focusing on the A-model, and explores the construction of quantum Z-local systems related to algebraic cycles and their open questions.
Contribution
It connects the A-model Hodge theory with quantum Z-local systems and higher algebraic cycles, highlighting intrinsic properties and open problems.
Findings
Construction of quantum Z-local system on the canonical bundle of P^2
Discussion of intrinsic A-model Hodge theory aspects
Open questions on algebraic cycles in mirror symmetry
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 P^2, and suggest how this should be related to the higher algebraic cycles studied in our 2011 CNTP article "Algebraic K-theory of toric hypersurfaces".
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.