Geodesic
Determinantal Barlow surfaces and phantom categories
Journal of the European Mathematical Society, Tome 17 (2015) no. 7, pp. 1569-1592 Cet article a éte moissonné depuis la source EMS Press

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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.
DOI : 10.4171/jems/539
Classification : 14-XX, 18-XX
Keywords: Derived categories, exceptional collections, semiorthogonal decompositions, Hochschild homology, Barlow surfaces 
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     author = {Christian B\"ohning and Hans-Christian Graf von Bothmer and Ludmil Katzarkov and Pawel Sosna},
     title = {Determinantal {Barlow} surfaces and phantom categories},
     journal = {Journal of the European Mathematical Society},
     pages = {1569--1592},
     year = {2015},
     volume = {17},
     number = {7},
     doi = {10.4171/jems/539},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/539/}
}
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Christian Böhning; Hans-Christian Graf von Bothmer; Ludmil Katzarkov; Pawel Sosna. Determinantal Barlow surfaces and phantom categories. Journal of the European Mathematical Society, Tome 17 (2015) no. 7, pp. 1569-1592. doi: 10.4171/jems/539

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