A few remarks on the Generalized Vanishing Conjecture

  title={A few remarks on the Generalized Vanishing Conjecture},
  author={Michiel de Bondt},
  journal={Archiv der Mathematik},
  • M. D. Bondt
  • Published 13 June 2012
  • Mathematics
  • Archiv der Mathematik
AbstractWe show that the Generalized Vanishing Conjecture $$\forall_{m \ge 1} [\Lambda^m f^m = 0] \Longrightarrow \forall_{m \gg 0}[\Lambda^m (g f^m) = 0]$$for a fixed differential operator $${\Lambda \in k[\partial]}$$ follows from a special case of it, namely that the additional factor g is a power of the radical polynomial f. Next we show that in order to prove the Generalized Vanishing Conjecture (up to some bound on the degree of Λ), we may assume that Λ is a linear combination of powers… 
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