Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 050-01. Ample rank-two bundles on the quadric surface without Griffiths-positive metrics
Manuscript map · lines 3515–3524
OpenAI@2026-10-07#rem:oai-p-050-01
Authors: OpenAI. Family 050.
Title: Ample rank-two bundles on the quadric surface without Griffiths-positive metrics.
Abstract: 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.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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