Real Algebraic and Analytic Geometry |

Euler characteristic of real non degenerate tropical complete intersections.

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Submission: 2007, November 6.

*Abstract:
We define nondegenerate tropical complete intersections imitating the
corresponding definition in complex algebraic geometry. As in the complex
situation, all nonzero intersection multiplicity numbers between tropical
hypersurfaces defining a nondegenerate tropical complete intersection are
equal to $1$. The intersection multiplicity numbers we use are sums of mixed
volumes of polytopes which are dual to cells of the tropical hypersurfaces.
We show that the Euler characteristic of a real nondegenerate tropical
complete intersection depends only on the Newton polytopes of the tropical
polynomials which define the intersection. Basically, it is equal to the
usual signature of a complex complete intersection with same Newton
polytopes, when this signature is defined. The proof reduces to the toric
hypersurface case, and uses the notion of $E$-polynomials of complex
varieties.*

**Full text**, 30p.:
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