{"title":"一类极大Albanese维数的最终准正则映射","authors":"G. Farkas","doi":"10.14231/AG-2019-014","DOIUrl":null,"url":null,"abstract":"Let $X$ be a smooth complex projective variety such that the Albanese map of $X$ is generically finite onto its image. Here we study the so-called eventual $m$-paracanonical map of $X$ (when $m=1$ we also assume $\\chi(K_X)>0$). We show that for $m=1$ this map behaves in a similar way to the canonical map of a surface of general type, while it is birational for $m>1$. We also describe it explicitly in several examples.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"The eventual paracanonical map of a variety of maximal Albanese dimension\",\"authors\":\"G. Farkas\",\"doi\":\"10.14231/AG-2019-014\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $X$ be a smooth complex projective variety such that the Albanese map of $X$ is generically finite onto its image. Here we study the so-called eventual $m$-paracanonical map of $X$ (when $m=1$ we also assume $\\\\chi(K_X)>0$). We show that for $m=1$ this map behaves in a similar way to the canonical map of a surface of general type, while it is birational for $m>1$. We also describe it explicitly in several examples.\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2019-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.14231/AG-2019-014\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.14231/AG-2019-014","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
The eventual paracanonical map of a variety of maximal Albanese dimension
Let $X$ be a smooth complex projective variety such that the Albanese map of $X$ is generically finite onto its image. Here we study the so-called eventual $m$-paracanonical map of $X$ (when $m=1$ we also assume $\chi(K_X)>0$). We show that for $m=1$ this map behaves in a similar way to the canonical map of a surface of general type, while it is birational for $m>1$. We also describe it explicitly in several examples.
期刊介绍:
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.