Singularities of Amoeba Contours

@misc{nisse2026singularities,
  title = {{Singularities of Amoeba Contours}},
  author = {Mounir Nisse},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.03601},
  eprint = {2608.03601},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.03601},
}

TY  - UNPB
TI  - Singularities of Amoeba Contours
AU  - Mounir Nisse
PY  - 2026
DA  - 2026/10/11
PB  - arXiv
DO  - 10.48550/arxiv.2608.03601
UR  - https://arxiv.org/abs/2608.03601
AB  - We give explicit real-algebraic equations for computing the singularities of amoeba contours, separating degeneracies of the logarithmic critical locus from coincidences of distinct critical lifts. For plane curves, this yields practical systems detecting nodes, cusps, and multiple branches. We also show that maximal sparsity does not maximize contour singularities, even for lattice triangles and parallelograms.
ER  -