Abstract
We discuss to what extent the local techniques of resolution of singularities over fields of characteristic zero can be applied to improve singularities in general. For certain interesting classes of singularities, this leads to an embedded resolution via blowing ups in regular centers. We illustrate this for generic determinantal varieties. The article is partially expository and is addressed to non-experts who aim to construct resolutions for other special classes of singularities in positive or mixed characteristic.
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Acknowledgements
The author heartily thanks Bernhard Dietel for many discussions and explanations on his thesis. He is grateful to Edward Bierstone, Anne Frühbis-Krüger, and Ulrich Görtz for many useful comments on an earlier draft of the paper. Further, he thanks the University of Mainz and the University of Versailles for their support and excellent working environment during his time there, when major parts of the article were developed.
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Supported by Research Fellowships of the Deutsche Forschungsgemeinschaft (SCHO 1595/1-1 and SCHO 1595/2-1).
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Schober, B. Partial Local Resolution by Characteristic Zero Methods. Results Math 73, 48 (2018). https://doi.org/10.1007/s00025-018-0808-7
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DOI: https://doi.org/10.1007/s00025-018-0808-7