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15 June 2020 The Noether inequality for algebraic 3 -folds
Jungkai A. Chen, Meng Chen, Chen Jiang
Duke Math. J. 169(9): 1603-1645 (15 June 2020). DOI: 10.1215/00127094-2019-0080

Abstract

We establish the Noether inequality for projective 3 -folds, and, specifically, we prove that the inequality vol ( X ) 4 3 p g ( X ) 10 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.

Citation

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Jungkai A. Chen. Meng Chen. Chen Jiang. "The Noether inequality for algebraic 3 -folds." Duke Math. J. 169 (9) 1603 - 1645, 15 June 2020. https://doi.org/10.1215/00127094-2019-0080

Information

Received: 15 September 2018; Revised: 23 July 2019; Published: 15 June 2020
First available in Project Euclid: 8 May 2020

zbMATH: 07226648
MathSciNet: MR4105534
Digital Object Identifier: 10.1215/00127094-2019-0080

Subjects:
Primary: 14E05
Secondary: 14J30

Rights: Copyright © 2020 Duke University Press

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Vol.169 • No. 9 • 15 June 2020
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