TY - JOUR
T1 - Exceptional Collection of Objects on Some Fake Projective Planes
AU - Lai, Ching Jui
AU - Yeung, Sai Kee
N1 - Funding Information:
This work was supported by the MOST [108-2115-M-006-016 to C.-J. L.]; the National Cheng Kung University; and fundings to S-K. Y. from the National Science Foundation. This work is partially done during the 1st author’s visit at National Center of Theoretical Science in Taiwan and the 2nd author’s visit of the Institute of Mathematics of the University of Hong Kong during the summers of 2013 and 2014. The authors thank the warm hospitality of the institutes. The authors would also like to thank the referees for helpful comments.
Publisher Copyright:
© The Author(s) 2021. Published by Oxford University Press. All rights reserved.
PY - 2022/11/1
Y1 - 2022/11/1
N2 - The purpose of this article is to explain a new method to establish the existence of an exceptional collection of length three for a fake projective plane M with nontrivial automorphism group, related to a conjecture of Galkin–Katzarkov–Mellit–Shinder in 2015. Our method shows that thirty fake projective planes support such a sequence, most of which are new. In particular, this provides many new H-phantom categories.
AB - The purpose of this article is to explain a new method to establish the existence of an exceptional collection of length three for a fake projective plane M with nontrivial automorphism group, related to a conjecture of Galkin–Katzarkov–Mellit–Shinder in 2015. Our method shows that thirty fake projective planes support such a sequence, most of which are new. In particular, this provides many new H-phantom categories.
UR - http://www.scopus.com/inward/record.url?scp=85157981239&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85157981239&partnerID=8YFLogxK
U2 - 10.1093/imrn/rnab186
DO - 10.1093/imrn/rnab186
M3 - Article
AN - SCOPUS:85157981239
SN - 1073-7928
VL - 2022
SP - 17546
EP - 17590
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
IS - 22
ER -