Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8966141 | Advances in Mathematics | 2018 | 52 Pages |
Abstract
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.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Yalong Cao, Davesh Maulik, Yukinobu Toda,