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July 26, 2026Open Access

Nonproperness sets in a weighted-lift family of Keller maps

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Authors

SMSimon Marcus

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Overview

This working manuscript investigates nonproperness sets in Keller maps, highlighting distinct components.

Key Points

  • The aim is to determine the complete nonproperness set for a family of Keller maps derived from seed polynomials.
  • Reduced the inverse problem to a polynomial equation of degree deg p + 1.
  • Constructed explicit determinant-one subfamilies for generic fiber degrees n ≥ 4.
  • Analyzed generic fiber cardinalities along irreducible components.
  • For quadratic seeds, the nonproperness set S{F_p} forms an irreducible discriminant surface.
  • For seeds of degree three or higher, S_{F_p} has two irreducible components: the discriminant surface and an additional affine plane.
  • The subfamilies are inequivalent under polynomial automorphisms, detectable by fiber cardinalities.

Cite This Study

Simon Marcus (2026) studied this question.

synapsesocial.com/papers/6a65a890d3aea3239cd78ddchttps://doi.org/10.5281/zenodo.21534750
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