On P¹ × P¹, coordinatewise power pullbacks of an explicit rank-two bundle, tensored with O(1,1), are ample for every positive power yet admit no smooth strictly Griffiths-positive Hermitian metric for all sufficiently large powers.
On P¹ × P¹, coordinatewise power pullbacks of an explicit rank-two bundle, tensored with O(1,1), are ample for every positive power yet admit no smooth strictly Griffiths-positive Hermitian metric for all sufficiently large powers.
On P¹ × P¹, coordinatewise power pullbacks of an explicit rank-two bundle, tensored with O(1,1), are ample for every positive power yet admit no smooth strictly Griffiths-positive Hermitian metric for all sufficiently large powers.
If correct, disproves the modern formulation of Griffiths’ positivity conjecture already in rank two on a quadric surface.
Does an ample rank-two bundle on a smooth projective surface always admit a Griffiths-positive metric?
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OpenAI reports ample rank-two bundles without Griffiths-positive metrics
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