Details

Autor(en) / Beteiligte

• Davydow, Alex
• Grigoriev, Dima

Titel

Bounds on the Number of Connected Components for Tropical Prevarieties

Ist Teil von

• Discrete & computational geometry, 2017-03, Vol.57 (2), p.470-493

Ort / Verlag

New York: Springer US

Erscheinungsjahr

2017

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• For a tropical prevariety in R n 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 + 7 n - 1 3 n · d 3 n 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 .