A Note on Exceptional Unimodal Singularities and K3 Surfaces

We study the relation between the graded stable derived categories of 14 exceptional unimodal singularities and the derived categories of K3 surfaces obtained as compactifications of the Milnor fibers. As a corollary, we obtain a basis of the numerical Grothendieck group similar to the one given by Ebeling and Ploog [”McKay correspondence for the Poincaré series of Kleinian and Fuchsian singularities.” Mathematische Annalen 347, no. 3 (2010): 689–702. MR 2640048].