For every smooth projective effective orbifold curve X, the total descendant Gromov–Witten partition function Z_X satisfies the Jiang–Tseng Virasoro constraints L_kZ_X=0 for every integer k≥ -1, where L_k are the Virasoro operators associated with the orbifold Gromov–Witten theory of X.

Jiang–Tseng Virasoro conjecture

The conjecture asserts Virasoro constraints for Gromov–Witten theory of every smooth projective effective orbifold curve. Jiang and Tseng formulated the orbifold conjecture in 2007; the full curve case was not previously recorded as proved.

Known results

Relative Virasoro constraints were proved for all nonsingular ordinary target curves, with the absolute case as a specialization (2003).
Jiang and Tseng established evidence for orbifold targets, including classifying-stack cases and genus-zero constraints (2007).
Degree-zero constraints and applications were obtained for weighted projective stacks such as $\mathbb{P}(1,N)$ and $\mathbb{P}(1,1,N)$ (2008).

September 2026 claimed proof

The preprint Virasoro Constraints for Orbifold Curves claims the relative theory with relative conditions at ordinary points, implying the absolute Jiang–Tseng conjecture for the full class of smooth projective effective orbifold curves. It is an unrefereed preprint, so the claimed resolution remains unverified.

Current status (as of September 2026): The absolute and relative conjectures are claimed solved by an unrefereed preprint, but neither claim has been independently verified.

Jiang–Tseng Virasoro conjecture

Primary source

Additional references

Progress summary

Solutions 0