Skip to main content Accessibility help
×
Hostname: page-component-848d4c4894-8bljj Total loading time: 0 Render date: 2024-06-27T02:44:28.532Z Has data issue: false hasContentIssue false

Semi-Orthogonal Decomposition of a Derived Category of a 3-Fold With an Ordinary Double Point

Published online by Cambridge University Press:  25 October 2022

Hamid Abban
Affiliation:
Loughborough University
Gavin Brown
Affiliation:
University of Warwick
Alexander Kasprzyk
Affiliation:
University of Nottingham
Shigefumi Mori
Affiliation:
Kyoto University, Japan
Get access

Summary

We consider semi-orthogonal decompositions of derived categories for 3-dimensional projective varieties in the case when the varieties have ordinary double points.

Type
Chapter
Information
Recent Developments in Algebraic Geometry
To Miles Reid for his 70th Birthday
, pp. 183 - 215
Publisher: Cambridge University Press
Print publication year: 2022

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Beilinson, A. A.. Coherent sheaves on Pn and problems in linear algebra. Funktsional. Anal. i Prilozhen., 12(3):68–69, 1978.Google Scholar
Bökstedt, Marcel and Amnon Neeman. Homotopy limits in triangulated categories. Compositivo Math., 86(2):209–234, 1993.Google Scholar
Bondal, A. and D. Orlov. Semiorthogonal decompositions for algebraic varieties. 1995.Google Scholar
Bondal, A. I.. Representations of associative algebras and coherent sheaves. Izv. Akad. Nauk SSSR Ser. Mat., 53(1):25–44, 1989.Google Scholar
Bondal and M. van den Bergh. Generators and representability of functors in commutative and noncommutative geometry. Mosc. Math.. J., A., 3(1):1–36, 258, 2003.CrossRefGoogle Scholar
Daniel Christensen, J., Bernhard Keller, and Amnon Neeman. Failure of Brown representability in derived categories. Topology, 40(6):1339–1361, 2001.Google Scholar
Eisenbud. Homological algebra on a complete intersection, David, with an application to group representations. Trans. Amer. Math. Soc., 260(1):35–64, 1980.Google Scholar
Kapranov, M. M.. On the derived categories of coherent sheaves on some homogeneous spaces. Invent. Math., 92(3):479–508, 1988.Google Scholar
Kawamata, Yujiro. B-equivalence and equivalence. J. Differential Geom., 61(1):147–171, 2002.CrossRefGoogle Scholar
Kawamata, Yujiro. Birational geometry and derived categories. Surveys in differential geometry 2017. Celebrating the 50th anniversary of the Journal of Differential Geometry, volume 22 of Surv. Differ. Geom., pages 291–317. Int. Press, Somerville, MA, 2018.Google Scholar
Kawamata, Yujiro. On multi-pointed non-commutative deformations and Calabi-Yau threefolds. Compos. Math., 154(9):1815–1842, 2018.Google Scholar
Karmazyn, J., A. Kuznetsov, and E. Shinder. Derived categories of singular surfaces. 2018.Google Scholar
Kawamata, Yujiro, Katsumi Matsuda, and Kenji Matsuki. Introduction to the minimal model problem. Algebraic geometry, Sendai, 1985, volume 10 of Adv. Stud. Pure Math., pages 283–360. NorthHolland, Amsterdam, 1987.Google Scholar
Kuznetsov, A.. Derived categories of families of sextic del Pezzo surfaces. 2017.Google Scholar
Neeman. The connection between the theory localization theorem of Thomason, Amnon, Trobaugh and Yao and the smashing subcategories of Bousfield and Ravenel. Ann. Sci. Ecole Norm. Sup. (4), 25(5):547–566, 1992.Google Scholar
Neeman, Amnon. The Grothendieck duality theorem via Bousfield's techniques and Brown representability. J. Amer. Math. Soc., 9(1):205–236, 1996.Google Scholar
O. Orlov. Triangulated categories of singularities and D-branes in Landau-Ginzburg models. Tr. Mat. Inst. Steklova, 246(Algebr. Geom. Metody, D., Svyazi i Prilozh.):240–262, 2004.Google Scholar
Orlov, Dmitri. Formal completions and idempotent completions of triangulated categories of singularities. Adv. Math., 226(1):206–217, 2011.Google Scholar
Ottaviani, Giorgio. Spinor bundles on quadrics. Trans. Amer. Math. Soc., 307(1):301–316, 1988.CrossRefGoogle Scholar
Toda, Yukinobu and Hokuto Uehara. Tilting generators via ample line bundles. Adv. Math., 223(1):1–29, 2010.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×