# Determinantal Barlow surfaces and phantom categories

Christian Böhning; Hans-Christian Graf von Bothmer; Ludmil Katzarkov; Pawel Sosna

Journal of the European Mathematical Society (2015)

- Volume: 017, Issue: 7, page 1569-1592
- ISSN: 1435-9855

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topBöhning, Christian, et al. "Determinantal Barlow surfaces and phantom categories." Journal of the European Mathematical Society 017.7 (2015): 1569-1592. <http://eudml.org/doc/277217>.

@article{Böhning2015,

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.},

author = {Böhning, Christian, Graf von Bothmer, Hans-Christian, Katzarkov, Ludmil, Sosna, Pawel},

journal = {Journal of the European Mathematical Society},

keywords = {derived categories; exceptional collections; semiorthogonal decompositions; Hochschild homology; Barlow surfaces; derived categories; exceptional collections; semiorthogonal decompositions; Hochschild homology; Barlow surfaces},

language = {eng},

number = {7},

pages = {1569-1592},

publisher = {European Mathematical Society Publishing House},

title = {Determinantal Barlow surfaces and phantom categories},

url = {http://eudml.org/doc/277217},

volume = {017},

year = {2015},

}

TY - JOUR

AU - Böhning, Christian

AU - Graf von Bothmer, Hans-Christian

AU - Katzarkov, Ludmil

AU - Sosna, Pawel

TI - Determinantal Barlow surfaces and phantom categories

JO - Journal of the European Mathematical Society

PY - 2015

PB - European Mathematical Society Publishing House

VL - 017

IS - 7

SP - 1569

EP - 1592

AB - 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.

LA - eng

KW - derived categories; exceptional collections; semiorthogonal decompositions; Hochschild homology; Barlow surfaces; derived categories; exceptional collections; semiorthogonal decompositions; Hochschild homology; Barlow surfaces

UR - http://eudml.org/doc/277217

ER -

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