Exceptional collections on Dolgachev surfaces associated with degenerations

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dc.contributor.authorCho, Yonghwako
dc.contributor.authorLee, Yongnamko
dc.date.accessioned2018-01-30T05:48:37Z-
dc.date.available2018-01-30T05:48:37Z-
dc.date.created2018-01-15-
dc.date.created2018-01-15-
dc.date.issued2018-01-
dc.identifier.citationADVANCES IN MATHEMATICS, v.324, pp.394 - 436-
dc.identifier.issn0001-8708-
dc.identifier.urihttp://hdl.handle.net/10203/239451-
dc.description.abstractDolgachev surfaces are simply connected minimal elliptic surfaces with p(g) = q = 0 and of Kodaira dimension 1. These surfaces are constructed by logarithmic transformations of rational elliptic surfaces. In this paper, we explain the construction of Dolgachev surfaces via Q-Gorenstein smoothing of singular rational surfaces with two cyclic quotient singularities. This construction is based on the paper [25]. Also, some exceptional bundles on Dolgachev surfaces associated with Q-Gorenstein smoothing have been constructed based on the idea of Hacking [12]. In the case if Dolgachev surfaces were of type (2,3), we describe the Picard group and present an exceptional collection of maximal length. Finally, we prove that the presented exceptional collection is not full, hence there exists a nontrivial phantom category in the derived category. (C) 2017 Elsevier Inc. All rights reserved.-
dc.languageEnglish-
dc.publisherACADEMIC PRESS INC ELSEVIER SCIENCE-
dc.subjectGENERAL TYPE-
dc.subjectALGEBRAIC-SURFACES-
dc.subjectENRIQUES SURFACES-
dc.subjectVECTOR-BUNDLES-
dc.subjectLINE BUNDLES-
dc.subjectSINGULARITIES-
dc.subjectCATEGORIES-
dc.subjectDEFORMATIONS-
dc.titleExceptional collections on Dolgachev surfaces associated with degenerations-
dc.typeArticle-
dc.identifier.wosid000418780700012-
dc.identifier.scopusid2-s2.0-85035311510-
dc.type.rimsART-
dc.citation.volume324-
dc.citation.beginningpage394-
dc.citation.endingpage436-
dc.citation.publicationnameADVANCES IN MATHEMATICS-
dc.identifier.doi10.1016/j.aim.2017.11.012-
dc.contributor.localauthorLee, Yongnam-
dc.description.isOpenAccessN-
dc.type.journalArticleArticle-
dc.subject.keywordAuthorQ-Gorenstein smoothing-
dc.subject.keywordAuthorDolgachev surfaces-
dc.subject.keywordAuthorExceptional collections-
dc.subject.keywordAuthorDerived categories-
dc.subject.keywordAuthorPhantom categories-
dc.subject.keywordPlusGENERAL TYPE-
dc.subject.keywordPlusALGEBRAIC-SURFACES-
dc.subject.keywordPlusENRIQUES SURFACES-
dc.subject.keywordPlusVECTOR-BUNDLES-
dc.subject.keywordPlusLINE BUNDLES-
dc.subject.keywordPlusSINGULARITIES-
dc.subject.keywordPlusCATEGORIES-
dc.subject.keywordPlusDEFORMATIONS-
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