@article{b309a99aa01b4bbe972f01b5ef5a43ed,
title = "The noether inequality for algebraic 3-folds",
abstract = "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.",
author = "Chen, {Jungkai A.} and Meng Chen and Chen Jiang and J{\'a}nos Koll{\'a}r",
note = "Funding Information: The first author was partially supported by the Ministry of Science and Technology and the National Center for Theoretical Sciences of Taiwan. The second author was supported by National Natural Science Foundation of China grants 11571076 and 11731004, by Program of Shanghai Subject Chief Scientist grant 16XD1400400, and by the Laboratory of Mathematics for Nonlinear Science, Fudan University. The third author was supported by Japan Society for the Promotion of Science KAKENHI grant JP16K17558 and by the World Premier International Research Center Initiative, MEXT, Japan. Publisher Copyright: {\textcopyright} 2020 Duke University Press. All rights reserved.",
year = "2020",
doi = "10.1215/00127094-2019-0080",
language = "English (US)",
volume = "69",
pages = "1603--1645",
journal = "Duke Mathematical Journal",
issn = "0012-7094",
publisher = "Duke University Press",
number = "9",
}