One-Parameter Toric Deformations of Cyclic Quotient Singularities

Details One-Parameter Toric Deformations of Cyclic Quotient Singularities One-Parameter Toric Deformations of Cyclic Quotient Singularities

2008-01-15

arxiv.org/abs/0801.2370v3

Journal of Pure and Applied Algebra, Volume 213 (2009), pp. 1086-1096

Mathematics

Algebraic Geometry

18 pages, 3 figures; v2 minor revisions; v3 strengthened main theorem

Scientific paper

10.1016/j.jpaa.2008.11.010

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.

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