{"title":"SINGULAR HOLOMORPHIC MORSE INEQUALITIES ON NON-COMPACT MANIFOLDS","authors":"Dan Coman, G. Marinescu, Hua Wang","doi":"10.59277/rrmpa.2023.61.82","DOIUrl":null,"url":null,"abstract":"We obtain asymptotic estimates of the dimension of cohomology on possibly non-compact complex manifolds for line bundles endowed with Hermitian metrics with algebraic singularities. We give a unified approach to establishing singular holomorphic Morse inequalities for hyperconcave manifolds, pseudoconvex domains, q-convex manifolds and q-concave manifolds, and we generalize related estimates of Berndtsson. We also consider the case of metrics with more general than algebraic singularities.","PeriodicalId":45738,"journal":{"name":"REVUE ROUMAINE DE MATHEMATIQUES PURES ET APPLIQUEES","volume":"160 1","pages":""},"PeriodicalIF":0.2000,"publicationDate":"2023-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"REVUE ROUMAINE DE MATHEMATIQUES PURES ET APPLIQUEES","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.59277/rrmpa.2023.61.82","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
We obtain asymptotic estimates of the dimension of cohomology on possibly non-compact complex manifolds for line bundles endowed with Hermitian metrics with algebraic singularities. We give a unified approach to establishing singular holomorphic Morse inequalities for hyperconcave manifolds, pseudoconvex domains, q-convex manifolds and q-concave manifolds, and we generalize related estimates of Berndtsson. We also consider the case of metrics with more general than algebraic singularities.
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