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arXiv · 0801.2370

One-Parameter Toric Deformations of Cyclic Quotient Singularities

Nathan Ilten
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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.

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Nathan Ilten. 2008-10-17. One-Parameter Toric Deformations of Cyclic Quotient Singularities. https://doi.org/10.1016/j.jpaa.2008.11.010

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