{"title":"关于维数为$$\\ge 3$$的环状DM堆上的$$text\\rm{H}-$$琐细线束","authors":"Lev Borisov, Chengxi Wang","doi":"10.1007/s00229-024-01583-x","DOIUrl":null,"url":null,"abstract":"<p>We study line bundles on smooth toric Deligne-Mumford stacks <span>\\({\\mathbb {P}}_{\\mathbf {\\Sigma }}\\)</span> of arbitrary dimension. We give a sufficient condition for when infinitely many line bundles on <span>\\({\\mathbb {P}}_{\\mathbf {\\Sigma }}\\)</span> have trivial cohomology. In dimension three, this sufficient condition is also a necessary condition under the technical assumption that <span>\\(\\mathbf {\\Sigma }\\)</span> has no more than one pair of collinear rays.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"5 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On $$\\\\textrm{H}-$$ trivial line bundles on toric DM stacks of dim $$\\\\ge 3$$\",\"authors\":\"Lev Borisov, Chengxi Wang\",\"doi\":\"10.1007/s00229-024-01583-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We study line bundles on smooth toric Deligne-Mumford stacks <span>\\\\({\\\\mathbb {P}}_{\\\\mathbf {\\\\Sigma }}\\\\)</span> of arbitrary dimension. We give a sufficient condition for when infinitely many line bundles on <span>\\\\({\\\\mathbb {P}}_{\\\\mathbf {\\\\Sigma }}\\\\)</span> have trivial cohomology. In dimension three, this sufficient condition is also a necessary condition under the technical assumption that <span>\\\\(\\\\mathbf {\\\\Sigma }\\\\)</span> has no more than one pair of collinear rays.</p>\",\"PeriodicalId\":49887,\"journal\":{\"name\":\"Manuscripta Mathematica\",\"volume\":\"5 1\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-07-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Manuscripta Mathematica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00229-024-01583-x\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Manuscripta Mathematica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00229-024-01583-x","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
On $$\textrm{H}-$$ trivial line bundles on toric DM stacks of dim $$\ge 3$$
We study line bundles on smooth toric Deligne-Mumford stacks \({\mathbb {P}}_{\mathbf {\Sigma }}\) of arbitrary dimension. We give a sufficient condition for when infinitely many line bundles on \({\mathbb {P}}_{\mathbf {\Sigma }}\) have trivial cohomology. In dimension three, this sufficient condition is also a necessary condition under the technical assumption that \(\mathbf {\Sigma }\) has no more than one pair of collinear rays.
期刊介绍:
manuscripta mathematica was founded in 1969 to provide a forum for the rapid communication of advances in mathematical research. Edited by an international board whose members represent a wide spectrum of research interests, manuscripta mathematica is now recognized as a leading source of information on the latest mathematical results.