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.
Original language | English (US) |
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Pages (from-to) | 1569-1592 |
Number of pages | 24 |
Journal | Journal of the European Mathematical Society |
Volume | 17 |
Issue number | 7 |
DOIs | |
State | Published - 2015 |
Keywords
- Barlow surfaces
- Derived categories
- Exceptional collections
- Hochschild homology
- Semiorthogonal decompositions
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics