## Rational homology manifolds and hypersurface normalizations

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## Abstract:

We prove a criterion for determining whether the normalization of a complex analytic space on which the shifted constant sheaf is perverse is a rational homology manifold, using a perverse sheaf known as the multiple-point complex. This perverse sheaf is naturally associated to any space on which the shifted constant sheaf is perverse, and has several interesting connections with the Milnor monodromy and mixed Hodge modules.## References

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## Additional Information

**Brian Hepler**- Affiliation: Department of Mathematics, Northeastern University, Boston, Massachusetts 02115
- MR Author ID: 1188759
- Email: hepler.b@husky.neu.edu
- Received by editor(s): May 8, 2018
- Received by editor(s) in revised form: August 7, 2018
- Published electronically: December 12, 2018
- Communicated by: Mark Behrens
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**147**(2019), 1605-1613 - MSC (2010): Primary 32S60, 32S35, 32S40, 32B10
- DOI: https://doi.org/10.1090/proc/14391
- MathSciNet review: 3910425