A counterexample to Griffiths’ positivity conjecture
The following describes the scope of the Lean formalization related to the following accompanying paper(s):
Scope
Griffiths' positivity conjecture predicts that every ample holomorphic vector bundle on a smooth complex projective variety admits a smooth Hermitian metric with strictly Griffiths-positive curvature. The formalized counterexample starts with a rank-two algebraic bundle $G$ on $\mathbb P^1\times\mathbb P^1$. Its coordinatewise power pullbacks, tensored with $\mathcal O(1,1)$, are ample for every positive power but admit no such metric for all sufficiently large powers.
The separate very-ampleness result for all admissible even exponents is not included.
Comparator links
| Result | Comparator statement |
|---|---|
| Ample bundles without Griffiths-positive metrics | QuadricBundles.lean |