OpenAI · 055-02 · 2026-09-24 · Algebraic and complex geometry
Prescribed large-volume charges on threefolds with trivial canonical bundle
preprints/Prescribed-large-volume-charges-on-threefolds-with-trivial-canonical-bundle-September-24-2026
Family 055. Toda's Gepner conjecture and large-volume stability.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Proves Toda's Gepner conjecture for every smooth complex quintic threefold, constructing a numerical Bridgeland stability condition with the prescribed phase shift . Also constructs numerical Bridgeland stability conditions at every sufficiently large volume on all smooth projective complex threefolds with trivial canonical bundle, with the exact ordinary and square-root-Todd central charges.
Let X be a smooth projective complex threefold with trivial canonical bundle. We construct numerical Bridgeland stability conditions with the exact ordinary and square-root-Todd central charges at every sufficiently large volume. One volume threshold works on an open set of real twists and ample directions. The resulting stability conditions have the support property on the full numerical Grothendieck group and stable point sheaves. Separately, on every smooth projective complex threefold we prove a strong tilt inequality above a volume threshold uniform in the object and twist along a fixed polarization.
Preprint source and Lean scope
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No Lean scope note is in the repository for this family. The preprint source below is still the full manuscript, not only the abstract. No compilation is asserted.