English

Exceptional bundles associated to degenerations of surfaces

Algebraic Geometry 2019-12-19 v1

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.

Keywords

Cite

@article{arxiv.1107.2644,
  title  = {Exceptional bundles associated to degenerations of surfaces},
  author = {Paul Hacking},
  journal= {arXiv preprint arXiv:1107.2644},
  year   = {2019}
}

Comments

19 pages