Towards the Green-Griffiths-Lang conjecture via equivariant localisation

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 $\mathrm{d}\mathrm{e}\mathrm{g}(X)\ge n^{9n}$.