The noether inequality for algebraic 3-folds

Jungkai A. Chen, Meng Chen, Chen Jiang, János Kollár

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We establish the Noether inequality for projective 3-folds, and, specifically, we prove that the inequality 4 10 vol.X / > 3 pg.X / -3 holds for all projective 3-folds X of general type with either pg.X / < 4 or pg.X / > 21, where pg.X / is the geometric genus and vol.X / is the canonical volume. This inequality is optimal due to known examples found by Kobayashi in 1992.

Original languageEnglish (US)
Pages (from-to)1603-1645
Number of pages43
JournalDuke Mathematical Journal
Issue number9
StatePublished - 2020

All Science Journal Classification (ASJC) codes

  • General Mathematics


Dive into the research topics of 'The noether inequality for algebraic 3-folds'. Together they form a unique fingerprint.

Cite this