Small Resolutions
A resolution of singularities
of a complex variety Y is called a small resolution if for every r>0, the space of points of Y where the fiber has dimension r is of codimension greater than 2r. Roughly speaking, this means that most fibers are small. In this case the morphism induces an isomorphism from the (intersection) homology of X to the intersection homology of Y (with the middle perversity).
There is a variety with two different small resolutions that have different ring structures on their cohomology, showing that there is in general no natural ring structure on intersection (co)homology.
Read more about this topic: Intersection Homology
Famous quotes containing the words small and/or resolutions:
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I throw down the chain of small stones! when life in my body has ceased,
I will go to Caoilte, and Conan, and Bran, Sceolan, Lomair,
And dwell in the house of the Fenians, be they in flames or at feast.”
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—Oscar Wilde (1854–1900)