On Delta for parameterized Curve Singularities
Abstract
We consider families of parameterizations of reduced curve singularities over a Noetherian base scheme and prove that the delta invariant is semicontinuous. In our setting, each curve singularity in the family is the image of a parameterization and not the fiber of a morphism. The problem came up in connection with the right-left classification of parameterizations of curve singularities defined over a field of positive characteristic. We prove a bound for right-left determinacy of a parameterization in terms of delta and the semicontinuity theorem provides a simultaneous bound for the determinacy in a family. The fact that the base space can be an arbitrary Noetherian scheme causes some difficulties but is (not only) of interest for computational purposes.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2021
- DOI:
- 10.48550/arXiv.2101.01784
- arXiv:
- arXiv:2101.01784
- Bibcode:
- 2021arXiv210101784G
- Keywords:
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- Mathematics - Algebraic Geometry;
- Mathematics - Commutative Algebra
- E-Print:
- Journal of Algebra, Volume 615, 2023, Pages 151-169, ISSN 0021-8693