The class of the cubic-homogenous mappings with nonzero constant Jacobian determinant is interesting because if it were proved that all mappings in this class are invertible, then the general Jacobian Conjecture would follow. A secondary conjecture was that all mappings in this class had linear invariants. De Bondt has recently put that to rest, with an example that has no linear invariants. Still, de Bondt's mapping has quadratic invariants. In this paper we exhibit an example in dimension 11 that has a cubic invariant but no quadratic (or linear) ones.

Search for homogeneous polynomial invariants and a cubic-homogeneous mapping without quadratic invariants

ZAMPIERI, Gaetano
2008-01-01

Abstract

The class of the cubic-homogenous mappings with nonzero constant Jacobian determinant is interesting because if it were proved that all mappings in this class are invertible, then the general Jacobian Conjecture would follow. A secondary conjecture was that all mappings in this class had linear invariants. De Bondt has recently put that to rest, with an example that has no linear invariants. Still, de Bondt's mapping has quadratic invariants. In this paper we exhibit an example in dimension 11 that has a cubic invariant but no quadratic (or linear) ones.
2008
Cubic-homogeneous maps; Linear dependence problem; Homogeneous polynomial invariants
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/321921
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact