Kavli Affiliate: Yukinobu Toda
| First 5 Authors: Yalong Cao, Yukinobu Toda, , ,
| Summary:
The Gopakumar-Vafa type invariants on Calabi-Yau 4-folds (which are
non-trivial only for genus zero and one) are defined by Klemm-Pandharipande
from Gromov-Witten theory, and their integrality is conjectured. In a previous
work of Cao-Maulik-Toda, $mathrm{DT}_4$ invariants with primary insertions on
moduli spaces of one dimensional stable sheaves are used to give a sheaf
theoretical interpretation of the genus zero GV type invariants. In this paper,
we propose a sheaf theoretical interpretation of the genus one GV type
invariants using descendent insertions on the above moduli spaces. The
conjectural formula in particular implies nontrivial constraints on genus zero
GV type (equivalently GW) invariants of CY 4-folds which can be proved by the
WDVV equation.
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