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Exceptional collections on some fake quadrics


Authors: Kyoung-Seog Lee and Timofey Shabalin
Journal: Proc. Amer. Math. Soc. 146 (2018), 2299-2313
MSC (2010): Primary 14F05; Secondary 14J29
DOI: https://doi.org/10.1090/proc/13705
Published electronically: March 9, 2018
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Abstract: We construct exceptional collections of maximal length on four families of surfaces of general type with $ p_g=q=0$ which are isogenous to a product of curves. From these constructions we obtain new examples of quasiphantom categories as their orthogonal complements.


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Additional Information

Kyoung-Seog Lee
Affiliation: Center for Geometry and Physics, Institute for Basic Science (IBS), Pohang 37673, Republic of Korea
Email: kyoungseog02@gmail.com

Timofey Shabalin
Affiliation: National Research University Higher School of Economics, AG Laboratory, 7 Vavilova street, Moscow, Russia, 117312
Email: shabalin.timofey@gmail.com

DOI: https://doi.org/10.1090/proc/13705
Keywords: Derived category, exceptional sequence, quasiphantom category, surfaces of general type, surfaces isogenous to a higher product
Received by editor(s): January 22, 2016
Received by editor(s) in revised form: October 5, 2016
Published electronically: March 9, 2018
Additional Notes: The first author was supported by Seoul National University via the Fellowship for Fundamental Academic Fields. He was supported by IBS-R003-Y1
The second author was partially supported by AG Laboratory HSE, RF government grant, ag. 11.G34.31.0023 and RScF grant, ag. 14-21-00053
Communicated by: Lev Borisov
Article copyright: © Copyright 2018 American Mathematical Society

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