# Exceptional collections on $\Sigma _{ 2 }$

@inproceedings{Ishii2021ExceptionalCO, title={Exceptional collections on \$\Sigma \_\{ 2 \}\$}, author={Akira Ishii and Shinnosuke Okawa and Hokuto Uehara}, year={2021} }

Structure theorems for exceptional objects and exceptional collections of the bounded derived category of coherent sheaves on del Pezzo surfaces are established by Kuleshov and Orlov in [KO94]. In this paper we propose conjectures which generalize these results to weak del Pezzo surfaces. Unlike del Pezzo surfaces, an exceptional object on a weak del Pezzo surface is not necessarily a shift of a sheaf and is not determined by its class in the Grothendieck group. Our conjectures explain how…

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