One-Parameter Toric Deformations of Cyclic Quotient Singularities
arXiv:0801.2370 · doi:10.1016/j.jpaa.2008.11.010
Abstract
In the case of two-dimensional cyclic quotient singularities, we classify all one-parameter toric deformations in terms of certain Minkowski decompositions. In particular, we describe to which components each such deformation maps, show how to induce each deformation from a versal family, give explicit equations for each deformation, describe the singularities in the general fibers, and construct the corresponding partial simultaneous resolutions.
18 pages, 3 figures; v2 minor revisions; v3 strengthened main theorem