Bounds on the Number of Connected Components for Tropical Prevarieties
نویسندگان
چکیده
For a tropical prevariety in R given by a system of k tropical polynomials in n variables with degrees at most d, we prove that its number of the connected components is less than ( k+7n−1 3n ) · d k+n+1 . On a number of 0-dimensional connected components a better bound ( k n ) · d n k−n+1 is obtained, which extends the Bezout bound due to B. Sturmfels from the case k = n to an arbitrary k ≥ n. Also we show that the latter bound is close to sharp, in particular, the number of connected components can depend on k.
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عنوان ژورنال:
- Discrete & Computational Geometry
دوره 57 شماره
صفحات -
تاریخ انتشار 2017