Genus zero Gopakumar–Vafa type invariants for Calabi–Yau 4-folds
Name
1801.02513.pdf
Description
Submitted version
Size
481.62 KB
Format
Adobe PDF
Checksum (MD5)
147ecc3a3b9cc36ba037b8e099b52389
Author(s)
Cao, Yalong
Maulik, Davesh
Toda, Yukinobu
Date Issued
2018
Journal
Advances in Mathematics
Publisher
Elsevier BV
Version
Original manuscript
Abstract
© 2018 Elsevier Inc. In analogy with the Gopakumar–Vafa conjecture on CY 3-folds, Klemm and Pandharipande defined GV type invariants on Calabi–Yau 4-folds using Gromov–Witten theory and conjectured their integrality. In this paper, we propose a sheaf-theoretic interpretation of their genus zero invariants using Donaldson–Thomas theory on CY 4-folds. More specifically, we conjecture genus zero GV type invariants are DT4 invariants for one-dimensional stable sheaves on CY 4-folds. Some examples are computed for both compact and non-compact CY 4-folds to support our conjectures. We also propose an equivariant version of the conjectures for local curves and verify them in certain cases.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1016/J.AIM.2018.08.013
