Deformation of Singularities and the Homology of Intersection Spaces

@article{Banagl2011DeformationOS,
  title={Deformation of Singularities and the Homology of Intersection Spaces},
  author={Markus Banagl and Laurenţiu Maxim},
  journal={arXiv: Algebraic Topology},
  year={2011}
}
While intersection cohomology is stable under small resolutions, both ordinary and intersection cohomology are unstable under smooth deformation of singularities. For complex projective algebraic hypersurfaces with an isolated singularity, we show that the first author's cohomology of intersection spaces is stable under smooth deformations in all degrees except possibly the middle, and in the middle degree precisely when the monodromy action on the cohomology of the Milnor fiber is trivial. In… 
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