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arXiv · 1509.03406

Towards the Green-Griffiths-Lang conjecture via equivariant localisation

Gergely Berczi
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Abstract

The Green-Griffiths-Lang conjecture says that for every complex projective algebraic variety $X$ of general type there exists a proper algebraic subvariety of $X$ containing all nonconstant entire holomorphic curves $f:\mathbb{C} \to X$. Using equivariant localisation on the Demailly-Semple jet differentials bundle we give an affirmative answer to this conjecture for generic projective hypersurfaces $X \subset \mathbb{P}^{n+1}$ of degree $\mathrm{deg}(X) \ge n^{9n}$.

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Gergely Berczi. 2015-09-11. Towards the Green-Griffiths-Lang conjecture via equivariant localisation. https://doi.org/10.1112/plms.12197

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