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Working paper

Exceptional collections of line bundles on the Beauville surface

arxiv.org. math. Cornell University, 2012. No. 1210.3339.
Galkin S., Shinder E.
We construct quasi-phantom admissible subcategories in the derived category of coherent sheaves on the Beauville surface S. These quasi-phantoms subcategories appear as right orthogonals to subcategories generated by exceptional collections of maximal possible length 4 on S. We prove that there are exactly 6 exceptional collections consisting of line bundles (up to a twist) and these collections are spires of two helices.