Exceptional bundles associated to degenerations of surfaces

Abstract

We study degenerations of complex surfaces with no vanishing cycles first described by J. Wahl. Given such a degeneration, we construct an exceptional vector bundle on the general fiber $Y$ in the case $H^{2,0}\left(Y\right)=H^1\left(Y\right)=0$. For $Y={\mathbb{P}}^2$, we show that our construction establishes a bijective correspondence between the possible singular surfaces and the set of exceptional bundles on $Y$ modulo a natural equivalence relation.