Gross–Joyce–Tanaka wall-crossing conjecture
The conjecture asserts that the Gross–Joyce–Tanaka wall-crossing formula holds for equivariant Donaldson–Thomas invariants of Calabi–Yau categories equipped with framing functors, as stability conditions cross walls. The supplied sources do not state the explicit wall-crossing identity or its full hypotheses.
References
Primary source
Additional references
Progress summary
A new preprint claims to settle the Gross–Joyce–Tanaka wall-crossing conjecture, but the result has not yet been independently checked.
The conjecture concerns wall-crossing formulas for Donaldson–Thomas invariants of Calabi–Yau fourfolds. Its original formulation is identified in a 2020 paper.
Known results
- A 2021 paper proved general wall-crossing formulas for quivers, curves, surfaces, Fano threefolds, and pairs, while treating the Calabi–Yau fourfold extension as prospective.
- A 2025 preprint claimed proofs for Calabi–Yau fourfold dg-quivers and local Calabi–Yau fourfolds, plus a reduction for semistable torsion-free sheaves on arbitrary Calabi–Yau fourfolds.
August 2026 claimed proof
A new preprint, Wall-crossing for equivariant DT4 invariants, claims the equivariant formula and constructs Calabi–Yau fourfold pullback virtual classes using Jouanolou devices, presenting this as a rigorous theorem in a broad DT4 framework. This is an unrefereed claim; no independent verification or counterexample was found. It appears to address the workaround that the 2025 preprint described as forthcoming.
Current status (as of August 2026): A preprint claims a full proof, but the conjecture remains unsettled pending independent verification.
Solutions 0
No solutions have been posted yet.