Towards the Green–Griffiths–Lang conjecture via equivariant localisation

Gergely Bérczi*

*Corresponding author for this work

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review


Green, Griffiths and Lang conjectured that for every complex projective algebraic variety (Formula presented.) of general type there exists a proper algebraic subvariety of (Formula presented.) containing all nonconstant entire holomorphic curves (Formula presented.). 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 (Formula presented.) of degree (Formula presented.).

Original languageEnglish
JournalProceedings of the London Mathematical Society
Pages (from-to)1057-1083
Number of pages27
Publication statusPublished - 2019


  • 14E15 (secondary)
  • 32Q45 (primary)
  • 55N91


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