AI Proof WatchKeep up with AI contributions

Virasoro constraints for smooth projective complete intersections

Do smooth complete intersections in complex projective space satisfy ordinary unreduced descendant Virasoro constraints coefficient by coefficient in every genus and curve class? The target includes arbitrary cohomology insertions, including primitive and odd classes.

Why it matters and what counts as progress

Why it matters: The all-genus complete-intersection target extends known special cases while retaining primitive and odd cohomology insertions.

What counts as progress: Prove the constraints in new genera or complete-intersection families, or establish the full insertion scope without replacing unreduced invariants.

How the problem developed

  1. 12 Mar 1997 · Conjecture [1]

    Tohru Eguchi, Kentaro Hori and Chuan-Sheng Xiong Proposed Virasoro constraints for general Fano quantum cohomology and constructed them in projective-space and related cases.

  2. 24 Sept 2026 · Reported claim [2]

    OpenAI Reported ordinary descendant Virasoro constraints for smooth projective complete intersections in every genus and curve class, including primitive and odd insertions, without a semisimplicity assumption.

AI contribution

Sources

  1. Eguchi, Hori and Xiong, Quantum Cohomology and Virasoro Algebra
  2. OpenAI, Virasoro Constraints for Projective Complete Intersections
  3. Virasoro Constraints for Projective Complete Intersections
  4. OpenAI, The Virasoro conjecture for smooth complete intersections in projective space (and its transfer to projective bundles)
  5. OpenAI mathematics release and provenance
Website timeline

Publication dates and editorial changes.