{"id":"openai-math/ample-rank-two-bundles-on-the-quadric-surface-without-griffiths-positive-metrics","pdf":"https://github.com/openai/math/blob/main/preprints/ample-rank-two-bundles-on-the-quadric-surface-without-griffiths-positive-metrics-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/ample-rank-two-bundles-on-the-quadric-surface-without-griffiths-positive-metrics-September-24-2026","tags":["complex-geometry","vector-bundles","griffiths-positivity"],"score":0,"title":"Ample rank-two bundles on the quadric surface without Griffiths-positive metrics","domain":"Algebraic and complex geometry","family":"050","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AG","summary":"We give counterexamples to Griffiths' conjecture in rank two on the quadric surface $`\\mathbb P^1\\times\\mathbb P^1`$. We construct an explicit bundle G whose coordinatewise power pullbacks, tensored with $`\\mathcal O(1,1)`$, are ample for every positive power, but admit no smooth strictly Griffiths-positive Hermitian metric for all sufficiently large powers.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":true,"family_title":"A counterexample to Griffiths’ positivity conjecture"}