Determinantal Barlow surfaces and phantom categories

Böhning, 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 -