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Determinantal Barlow surfaces and phantom categories

Christian BöhningHans-Christian Graf von BothmerLudmil KatzarkovPawel Sosna — 2015

Journal of the European Mathematical Society

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....

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