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There is a number of "aesthetically similar" topics in combinatorial algebraic
geometry, such as toric complete intersections, hyperplane arrangements, simplest
singularity strata of general polynomial maps, some discriminant and incidence
varieties in enumerative geometry and polynomial optimization, polynomial ODEs such as
reaction networks, generalized Calabi--Yau complete intersections.
I will talk about a convenient umbrella generality for all of them, which still admits a version of the classical theory of Newton polytopes (but with so-called tropical complete intersections instead of polytopes). This generalization includes the BKK formula, the patchworking construction, and other familiar tools, but applies to many new interesting objects. https://arxiv.org/abs/2212.00320 |