The Noether inequality for algebraic threefolds (With an Appendix by J��nos Koll��r)
| Autor: | Chen, Jungkai A., Chen, Meng, Jiang, Chen |
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| Rok vydání: | 2018 |
| Předmět: | |
| DOI: | 10.48550/arxiv.1803.05553 |
| Popis: | We establish the Noether inequality for projective $3$-folds. More precisely, we prove that the inequality $${\rm vol}(X)\geq \tfrac{4}{3}p_g(X)-{\tfrac{10}{3}}$$ holds for all projective $3$-folds $X$ of general type with either $p_g(X)\leq 4$ or $p_g(X)\geq 21$, where $p_g(X)$ is the geometric genus and ${\rm vol}(X)$ is the canonical volume. This inequality is optimal due to known examples found by M. Kobayashi in 1992. v1: 48 pages, comments are welcome; v2: defn. 2.4 corrected, minor changes made to the proofs of 5.9, 5.10; v3: 34 pages, original sect. 3 and appendix were replaced by an appendix by J\'{a}nos Koll\'{a}r, which simplified the proof and improved the main result; v4: 36 pages, final version to appear in Duke Math. J |
| Databáze: | OpenAIRE |
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