A Derived Equivalence For A Del Pezzo Surface Of Degree 6 Over An Arbitrary Field

Abstract

Let $S$ be a degree six del Pezzo surface over an arbitrary field $F$. Motivated by the first author's classification of all such $S$ up to isomorphism in terms of a separable $F$-algebra $B\times Q\times F$, and by his K-theory isomorphism $K_n(S)\cong K_n(B\times Q\times F)$ for $n\ge 0$, we prove an equivalence of derived categories $$ \sD^b(\coh S) \equiv \sD^b(\mod A) $$ where $A$ is an explicitly given finite dimensional $F$-algebra whose semisimple part is $B\times Q\times F$. Submitted to the Journal of K-theory