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摘要翻译：
我们模仿复代数几何中的相应定义，定义了非退化热带完全交。在复杂情况下，定义一个非退化热带完全交集的热带超曲面之间的所有非零交集重数都等于1。我们使用的交重数是热带超曲面单元对偶的多边形混合体积的和。证明了实非退化热带完全交集的欧拉特性仅依赖于定义交集的热带多项式的牛顿多边形。当定义这个符号时，它基本上等于具有相同牛顿多边形的复完全交的通常符号。证明归结为复曲面的情形，并使用复变体的$E$-多项式的概念。
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英文标题：
《Euler Characteristic of real nondegenerate tropical complete
intersections》
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作者：
Benoit Bertrand, Frederic Bihan
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics 数学
二级分类：Combinatorics 组合学
分类描述：Discrete mathematics, graph theory, enumeration, combinatorial optimization, Ramsey theory, combinatorial game theory
离散数学，图论，计数，组合优化，拉姆齐理论，组合对策论
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英文摘要：
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.
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PDF链接：
https://arxiv.org/pdf/0710.1222
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