Virasoro constraints for complete intersections and projective-bundle towers

Proves the full ordinary unreduced descendant Virasoro conjecture for smooth complete intersections in complex projective space, in every genus and curve class with arbitrary cohomology insertions. The constraints also pass from any smooth projective complex base satisfying them to the projectivization of every algebraic vector bundle of rank at least two, and hence to projective-bundle towers.

Manuscripts (2)

Virasoro Constraints under Projectivization

October 5, 2026 · source · cite as \cite{OAI:Virasoro-Constraints-under-Projectivization-October-5-2026}

We prove that full ordinary descendant Virasoro constraints pass from a smooth projective complex base to the projectivization of any algebraic vector bundle of rank at least two. The bundle need not split and satisfies no positivity requirement. Assuming the full constraints on the base, the conclusion includes every genus, each individual integral curve class, and all cohomology insertions, including primitive and odd classes. The result also applies successively to towers of projective bundles.

Virasoro Constraints for Projective Complete Intersections

September 24, 2026 · source · cite as \cite{OAI:Virasoro-Constraints-for-Projective-Complete-Intersections-September-24-2026}

We prove the Virasoro conjecture for the ordinary descendant Gromov–Witten theory of smooth complete intersections in projective space, in every genus and curve class and with arbitrary cohomology insertions. This includes primitive and odd cohomology classes, with no semisimplicity assumption.

Result 065 · Algebraic and complex geometry. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.