Exceptional bundles associated to degenerations of surfaces

Abstract

In 1981 J. Wahl described smoothings of surface quotient singularities with no vanishing cycles. Given a smoothing of a projective surface X of this type, we construct an associated exceptional vector bundle on the nearby fiber Y in the case H^{2,0}(Y)=H^1(Y)=0. If Y is the projective plane we show that our construction establishes a bijective correspondence between the possible degenerate surfaces X and exceptional bundles on Y modulo dualizing and tensoring by line bundles. If Y is of general type then our construction establishes a connection between components of the boundary of the moduli space of surfaces deformation equivalent to Y and exceptional bundles on Y.

19 pages

References in corpus (3)

• Smoothable del Pezzo surfaces with quotient singularities
• A simply connected surface of general type with p_g=0 and K^2=2
• Compact moduli of plane curves

Cited by in corpus (7)

• Scattering diagrams, stability conditions, and coherent sheaves on ${\mathbb{P}}^2$
• A note on degenerations of del Pezzo surfaces
• Combinatorial aspects of exceptional sequences on (rational) surfaces
• Exceptional collections on Dolgachev surfaces associated with degenerations
• Exceptional collections in surface-like categories
• Degenerations of Godeaux surfaces and exceptional vector bundles
• Orthogonal exceptional collections from $\mathbb{Q}$-Gorenstein degeneration of surfaces