{"title":"代数3 -折叠的Noether不等式","authors":"J. Chen, Meng Chen, Chen Jiang","doi":"10.1215/00127094-2019-0080","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2020-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"10","resultStr":"{\"title\":\"The Noether inequality for algebraic 3 -folds\",\"authors\":\"J. Chen, Meng Chen, Chen Jiang\",\"doi\":\"10.1215/00127094-2019-0080\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"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.\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2020-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"10\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1215/00127094-2019-0080\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1215/00127094-2019-0080","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
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.
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