The noether inequality for algebraic 3-folds

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

doi:10.1215/00127094-2019-0080

The noether inequality for algebraic 3-folds

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

Mathematics

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

We establish the Noether inequality for projective 3-folds, and, specifically, we prove that the inequality 4 10 vol.X / > ₃ p_g.X / -₃ holds for all projective 3-folds X of general type with either p_g.X / < 4 or p_g.X / > 21, where p_g.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 language	English (US)
Pages (from-to)	1603-1645
Number of pages	43
Journal	Duke Mathematical Journal
Volume	69
Issue number	9
DOIs	https://doi.org/10.1215/00127094-2019-0080
State	Published - 2020

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1215/00127094-2019-0080

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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.",

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AU - Chen, Jungkai A.

AU - Chen, Meng

AU - Jiang, Chen

AU - Kollár, János

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Y1 - 2020

N2 - 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.

AB - 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.

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SP - 1603

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JO - Duke Mathematical Journal

JF - Duke Mathematical Journal

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The noether inequality for algebraic 3-folds

Abstract

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