Donaldson-Thomas invariants of Calabi-Yau orbifolds under flops
Yunfeng Jiang
TL;DR
This paper proves that Donaldson-Thomas invariants of Calabi-Yau threefold Deligne-Mumford stacks remain unchanged under orbifold flops, a specific type of crepant birational transformation involving quotient singularities.
Contribution
It establishes the invariance of Donaldson-Thomas invariants under orbifold flops for Calabi-Yau threefold stacks, extending previous results to orbifold settings.
Findings
Donaldson-Thomas invariants are preserved under orbifold flops.
Orbifold flops involve quotient of weighted projective lines by cyclic groups.
Invariance holds for Calabi-Yau threefold Deligne-Mumford stacks.
Abstract
We study the Donaldson-Thomas type invariants for the Calabi-Yau threefold Deligne-Mumford stacks under flops. A crepant birational morphism between two smooth Calabi-Yau threefold Deligne-Mumford stacks is called an orbifold flop if the flopping locus is the quotient of weighted projective lines by a cyclic group action. We prove that the Donaldson-Thomas invariants are preserved under orbifold flops.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Geometry and complex manifolds