Kavli Affiliate: Yukinobu Toda
| First 5 Authors: Yalong Cao, Yukinobu Toda, , ,
| Summary:
Nagao-Nakajima introduced counting invariants of stable perverse coherent
systems on small resolutions of Calabi-Yau 3-folds and determined them on the
resolved conifold. Their invariants recover DT/PT invariants and Szendr"oi’s
non-commutative invariants in some chambers of stability conditions. In this
paper, we study an analogue of their work on Calabi-Yau 4-folds. We define
counting invariants for stable perverse coherent systems using primary
insertions and compute them in all chambers of stability conditions. We also
study counting invariants of local resolved conifold
$mathcal{O}_{mathbb{P}^1}(-1,-1,0)$ defined using torus localization and
tautological insertions. We conjecture a wall-crossing formula for them, which
upon dimensional reduction recovers Nagao-Nakajima’s wall-crossing formula on
resolved conifold.
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