Abstract
We prove that the blowup of the jet scheme of a singular hypersurface along a certain jet-related module is not an isomorphism. In conjunction with recent developments in the theory of Nash blowups, our result holds over fields of arbitrary characteristic. Our approach is based on explicit presentations given by a higher-order Jacobian matrix combined with a certain jet-related matrix.
Acknowledgments
We thank Roi Docampo and Takehiko Yasuda for their motivating comments and questions on a previous version of this paper. We also thank the referee for the careful reading, the nice remarks, and for drawing our attention to the reference [15].
Citation
Paul Barajas. Daniel Duarte. "A Nobile-like theorem for jet schemes of hypersurfaces." Osaka J. Math. 60 (3) 555 - 569, July 2023.
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