Abstract
We discuss how to resolve generic skew-symmetric and generic symmetric determinantal singularities. The key ingredients are (skew-) symmetry preserving matrix operations in order to deduce an inductive argument.
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Acknowledgements
Bernd Schober thanks Laura Escobar for joint discussions on (skew-) symmetry preserving decompositions of matrices in the context of a different topic which inspired the methods for reduction in the present article. Both authors thank the referees for useful comments on an earlier version of the article and in particular, for pointing out parts that needed clarification in the proof of Theorem A.
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B.S. was partially supported by the project “Order zeta functions and resolutions of singularities” funded by the Deutsche Forschungsgemeinschaft (DFG) (DFG Project Number: 373111162).
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Gaube, S.A., Schober, B. Desingularization of generic symmetric and generic skew-symmetric determinantal singularities. manuscripta math. (2024). https://doi.org/10.1007/s00229-024-01544-4
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DOI: https://doi.org/10.1007/s00229-024-01544-4