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Determinantal Barlow surfaces and phantom categories.

Determinantal Barlow surfaces and phantom categories.

Authors :
Böhning, Christian
von Bothmer, Hans-Christian Graf
Katzarkov, Ludmil
Sosna, Pawel
Source :
Journal of the European Mathematical Society (EMS Publishing); 2015, Vol. 17 Issue 7, p1569-1592, 24p
Publication Year :
2015

Abstract

We prove that the bounded derived category of the surface S constructed by Barlow admits a length 11 exceptional sequence consisting of (explicit) line bundles. Moreover, we show that in a small neighbourhood of S in the moduli space of determinantal Barlow surfaces, the generic surface has a semiorthogonal decomposition of its derived category into a length 11 exceptional sequence of line bundles and a category with trivial Grothendieck group and Hochschild homology, called a phantom category. This is done using a deformation argument and the fact that the derived endomorphism algebra of the sequence is constant. Applying Kuznetsov's results on heights of exceptional sequences, we also show that the sequence on S itself is not full and its (left or right) orthogonal complement is also a phantom category. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
14359855
Volume :
17
Issue :
7
Database :
Complementary Index
Journal :
Journal of the European Mathematical Society (EMS Publishing)
Publication Type :
Academic Journal
Accession number :
157481990
Full Text :
https://doi.org/10.4171/JEMS/539