Calculating Milnor Numbers and Versal Component Dimensions from P-Resolution Fans
Nathan Owen Ilten
TL;DR
This paper introduces a method to compute deformation invariants, including Milnor numbers and versal component dimensions, for two-dimensional cyclic quotient singularities using toric fan descriptions.
Contribution
It provides a new approach to calculating deformation invariants from P-resolution fans, enhancing understanding of singularity smoothings.
Findings
Calculated dimensions of versal base space components.
Determined Milnor numbers of smoothings.
Linked toric fan descriptions to deformation invariants.
Abstract
We use Altmann's toric fan description of P-resolutions to formulate a new description of deformation theory invariants for two-dimensional cyclic quotient singularities. In particular, we show how to calculate the dimensions of the (reduced) versal base space components as well as Milnor numbers of smoothings over them.
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