Toric degenerations and homotopy methods from finite Khovanskii bases
- Elise Walker (Texas A&M)
Homotopies are useful numerical methods for solving systems of polynomial equations. Embedded toric degenerations are one source for homotopy algorithms. In particular, if a projective variety has a toric degeneration, then linear sections of that variety can be optimally computed using the polyhedral homotopy. Any variety whose coordinate ring has a finite Khovanskii basis is known to have a toric degeneration. We provide embeddings for this Khovanskii toric degeneration to compute general linear sections of the variety. This is joint work with Michael Burr and Frank Sottile.