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Classification of full exceptional collections of line bundles on three blow-ups of P^3
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics. Center for Geometry and Physics, Institute for Basic Science (IBS) Pohang 37673, Korea. (Algebra och geometri)ORCID iD: 0000-0003-0999-5553
Center for Applied Mathematics, Tianjin University.
Center for Applied Mathematics, Tianjin University.
2019 (English)In: Journal of the Korean Mathematical Society, ISSN 0304-9914, E-ISSN 2234-3008, Vol. 56, no 2, p. 387-419Article in journal (Refereed) Published
Abstract [en]

A fullness conjecture of Kuznetsov says that if a smooth pro-jective variety X admits a full exceptional collection of line bundles oflength l, then any exceptional collection of line bundles of length l is full.In this paper, we show that this conjecture holds for X as the blow-upof P^3 at a point, a line, or a twisted cubic curve, i.e., any exceptionalcollection of line bundles of length 6 on X is full. Moreover, we obtainan explicit classification of full exceptional collections of line bundles onsuch X.

Place, publisher, year, edition, pages
Seoul, Korea, 2019. Vol. 56, no 2, p. 387-419
Keywords [en]
derived category of coherent sheaves, full exceptional collection, semiorthogonal decomposition
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-377691DOI: 10.4134/JKMS.j180204OAI: oai:DiVA.org:uu-377691DiVA, id: diva2:1291386
Available from: 2019-02-25 Created: 2019-02-25 Last updated: 2019-03-18Bibliographically approved

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Publisher's full texthttp://pdf.medrang.co.kr/kms01/JKMS/56/JKMS-56-2-387-419.pdf

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Liu, Wanmin

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