A Nullstellensatz for amoebas

@inproceedings{Purbhoo2006ANF,
  title={A Nullstellensatz for amoebas},
  author={Kevin Purbhoo},
  year={2006}
}
  • Kevin Purbhoo
  • Published 2006
  • Mathematics
  • The amoeba of an affine algebraic variety V in (C^*)^r is the image of V under the map (z_1, ..., z_r) -> (log|z_1|, ..., log|z_r|). We give a characterisation of the amoeba based on the triangle inequality, which we call testing for lopsidedness. We show that if a point is outside the amoeba of V, there is an element of the defining ideal which witnesses this fact by being lopsided. This condition is necessary and sufficient for amoebas of arbitrary codimension, as well as for… CONTINUE READING

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