DT-GV correspondence on the Mukai-Umemura variety
Kiryong Chung, Joonyeong Won
TL;DR
This paper computes Donaldson-Thomas invariants for a specific Calabi-Yau 4-fold, verifying theoretical predictions related to Gopakumar-Vafa invariants using localization techniques.
Contribution
It provides explicit calculations of DT invariants for the Mukai-Umemura variety and confirms conjectural relations with GV invariants under certain assumptions.
Findings
Verification of Cao, Maulik, and Toda's predictions
Explicit DT invariants for the Mukai-Umemure variety
Assumption of genus-one GV invariants vanishing
Abstract
We compute Donaldson-Thomas(DT) invariants and their descendant invariants for the local Calabi-Yau 4-fold over the Mukai-Umemura variety via several localization formulas. Assuming that the genus-one Gopakumar-Vafa(GV) type invariants vanish, our computations verify the predictions of Cao, Maulik, and Toda.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Geometry and complex manifolds