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The Green–Griffiths–Lang and Kobayashi hyperbolicity conjectures for generic hypersurfaces of polynomial degree are proved using intersection theory for non-reductive geometric invariant theoretic quotients and recent work of Riedl and Yang. [ABSTRACT FROM AUTHOR]

Green and Griffiths [ 25 ] and Lang [ 29 ] conjectured 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 |$f:{\mathbb{C}} \to X$|⁠. We construct a compactification of the invariant jet differentials bundle over complex manifolds motivated by an algebraic model of Morin singularities and we develop an iterated residue formula using equivariant localisation for tautological integrals over it. Using this we show that the polynomial Green–Griffiths–Lang conjecture for a generic projective hypersurface of degree |$\deg (X)>2n^{9}$| follows from a positivity conjecture for Thom polynomials of Morin singularities. [ABSTRACT FROM AUTHOR]

Green, Griffiths and Lang conjectured 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:C→X. Using equivariant localisation we develop an iterated residue formula for cohomological pairings on the Demailly–Semple jet bundle. We apply this formula and a strategy of Demailly to give affirmative answer to the Green–Griffiths–Lang conjecture for generic projective hypersurfaces X⊂Pn+1 of degree deg(X)⩾n9n. [ABSTRACT FROM AUTHOR]