We establish the Noether inequality for projective -folds, and, specifically, we prove that the inequality holds for all projective -folds of general type with either or , where is the geometric genus and is the canonical volume. This inequality is optimal due to known examples found by Kobayashi in 1992.
"The Noether inequality for algebraic -folds." Duke Math. J. 169 (9) 1603 - 1645, 15 June 2020. https://doi.org/10.1215/00127094-2019-0080