TILTING CHAINS OF NEGATIVE CURVES ON RATIONAL SURFACES

We introduce the notion of exact tilting objects, which are partial tilting objects $T$ inducing an equivalence between the abelian category generated by $T$ and the category of modules over the endomorphism algebra of $T$ . Given a chain of sufficiently negative rational curves on a rational surface, we construct an exceptional sequence whose universal extension is an exact tilting object. For a chain of $(-2)$ -curves, we obtain an equivalence with modules over a well-known algebra.