Computational issues

1. How to compute examples of amoebas and tropical varieties?
2. Special features to compute:
   • homology groups of the complement;
   • is there a Hermitean form whose signature is equal to the number of complement components?
3. Which classical varieties are expansive (i.e., is 0 is in the amoeba?) ? E.g.,
   • Grassmannians, generalized flag manifolds, spherical varieties, determinantal varieties, Schubert varieties;
   • Calabi-Yaus.
4. Develop the theory of smooth curves.
5. What is the complexity of deciding the vanishing of a resultant?
6. When does $\text{Log}(X)$ lie in a lower-dimensional subspace?
7. How hard is it to compute (i.e., what is the complexity of computing) the distance of a point to the discriminantal variety?

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