Abstract
We find a recursive formula for the motivic Milnor fiber of an irreducible plane curve, using the notions of a truncation and derived curve. We then apply natural transformations to obtain a similar recursion for the Hodge-theoretic spectrum.
Dedicated to Antonio Campillo on the occasion of his 65th birthday
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Acknowledgements
This paper benefited greatly from extensive conversations with Mirel Caibăr, and Alejandro Melle Hernández; we also received helpful advice from François Loeser. The first author was supported by Spanish Ministerio de Ciencia y Tecnología Grant no. MTM2016-76868-C2-1-P. The second author was supported by a Collaboration Grant from the Simons Foundation, and worked on this project while in residence at the Fields Institute.
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González Villa, M., Kennedy, G., McEwan, L.J. (2018). A Recursive Formula for the Motivic Milnor Fiber of a Plane Curve. In: Greuel, GM., Narváez Macarro, L., Xambó-Descamps, S. (eds) Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics. Springer, Cham. https://doi.org/10.1007/978-3-319-96827-8_9
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DOI: https://doi.org/10.1007/978-3-319-96827-8_9
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