A study in the resolution of singularity on a field with characteristic ≠ 2

Singularities in general are considered to be one of the important issues in algebraic geometry and applied mathematics, among them the ADE or simple singularities which drew attention since they have appeared separately in various areas of scientific applications. The name comes from three graphs characterized by letters A, D and E denoting types of Lie groups. Arnold stated them in a direct manner. Many people gave studies about the subject like Roczen.M who presented the canonical resolution in dimension 3 and Char ≠ 2. giving an equivalent non-singular variety is what meant by resolution, Canonical resolution adds a description of the exceptional loci.

Blowing-ups along exceptional curves

Let X be a 3-dimensional complex manifold(variety) , C ⊆ X an exceptional curve. We prove that 1 1 C ⊆ X is also an exceptional curve,where 1 C is a negative section corresponding to the exact sequence of And C I is an C O -ideal.