Thom polynomials of Morin singularities and the Green-Griffiths-Lang\n conjecture

2010/11/21 by Gergely Bérczi, Berczi, Gergely · 1 citation
Mathematics · #13A50 #32Q45 #55N91 #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1011.4710

openalex publication_date 2010/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Green-Griffiths-Lang conjecture says that for every complex projective\nalgebraic variety X of general type there exists a proper algebraic\nsubvariety of X containing all nonconstant entire holomorphic curves\nf:\ℂ \→ X. We construct a compactification of the invariant jet\ndifferentials bundle over complex manifolds motivated by an algebraic model of\nMorin singularities and we develop an iterated residue formula using\nequivariant localisation for tautological integrals over it. We show that the\npolynomial GGL conjecture for a generic projective hypersurface of degree\ndeg(X)>2n¹⁰ follows from a positivity conjecture for Thom\npolynomials of Morin singularities.\n

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• Effective algebraic degeneracy of entire curves in complements of smooth projective hypersurfaces

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