{"title":"非典型极化投影变体族的有界性结果","authors":"Kenneth Ascher, Behrouz Taji","doi":"arxiv-2408.15153","DOIUrl":null,"url":null,"abstract":"We prove that, over a smooth quasi-projective curve, the set of\nnon-isotrivial, smooth and projective families of polarized varieties with a\nfixed Hilbert polynomial and semi-ample canonical bundle is bounded. This\nextends the boundedness results of Arakelov, Parshin, and Kov\\'acs--Lieblich\nbeyond the canonically polarized case.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Boundedness results for families of non-canonically polarized projective varieties\",\"authors\":\"Kenneth Ascher, Behrouz Taji\",\"doi\":\"arxiv-2408.15153\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that, over a smooth quasi-projective curve, the set of\\nnon-isotrivial, smooth and projective families of polarized varieties with a\\nfixed Hilbert polynomial and semi-ample canonical bundle is bounded. This\\nextends the boundedness results of Arakelov, Parshin, and Kov\\\\'acs--Lieblich\\nbeyond the canonically polarized case.\",\"PeriodicalId\":501063,\"journal\":{\"name\":\"arXiv - MATH - Algebraic Geometry\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Algebraic Geometry\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2408.15153\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Algebraic Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.15153","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Boundedness results for families of non-canonically polarized projective varieties
We prove that, over a smooth quasi-projective curve, the set of
non-isotrivial, smooth and projective families of polarized varieties with a
fixed Hilbert polynomial and semi-ample canonical bundle is bounded. This
extends the boundedness results of Arakelov, Parshin, and Kov\'acs--Lieblich
beyond the canonically polarized case.
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