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Determinantal Barlow surfaces and phantom categories.
Determinantal Barlow surfaces and phantom categories.
- 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