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We use constructions of surfaces as abelian covers to write down exceptionalcollections of line bundles of maximal length for every surface $X$ in certainfamilies of surfaces of general type with $p_g=0$ and $K_X^2=3,4,5,6,8$. Wealso compute the algebra of derived endomorphisms for an appropriately chosenexceptional collection, and the Hochschild cohomology of the correspondingquasiphantom category. As a consequence, we see that the subcategory generatedby the exceptional collection does not vary in the family of surfaces. Finally,we describe the semigroup of effective divisors on each surface, answering aquestion of Alexeev.

Enumerating exceptional collections of line bundles on some surfaces of general type