实半稳定退化的欧拉特征与签名

IF 1.1 2区数学 Q1 MATHEMATICS

Journal of the Institute of Mathematics of Jussieu Pub Date : 2021-10-18 DOI:10.1017/S1474748022000056

Erwan Brugall'e

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引用次数: 5

摘要

摘要我们给出了一个原动力证明，对于非奇异实热带完全交，实部分的欧拉特征等于复部分的特征。Itenberg最初在$\mathbb中曲面的情况下证明了这一点{C}P^{3} $，并先后被Bertrand、Bihan和Bertrand推广。与以前的方法不同，我们的证明是半稳定退化的运动附近纤维的应用。特别地，它将Itenberg、Bertrand和Bihan的原始结果推广到承认$\mathbb｛Q｝$非奇异热带极限的真实分析族。

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EULER CHARACTERISTIC AND SIGNATURE OF REAL SEMI-STABLE DEGENERATIONS

Abstract We give a motivic proof of the fact that for nonsingular real tropical complete intersections, the Euler characteristic of the real part is equal to the signature of the complex part. This was originally proved by Itenberg in the case of surfaces in $\mathbb {C}P^{3}$ , and has been successively generalized by Bertrand and by Bihan and Bertrand. Our proof, different from previous approaches, is an application of the motivic nearby fiber of semistable degenerations. In particular, it extends the original result by Itenberg, Bertrand, and Bihan to real analytic families admitting a $\mathbb {Q}$ -nonsingular tropical limit.

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来源期刊

Journal of the Institute of Mathematics of Jussieu 数学-数学

CiteScore

2.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of the Institute of Mathematics of Jussieu publishes original research papers in any branch of pure mathematics; papers in logic and applied mathematics will also be considered, particularly when they have direct connections with pure mathematics. Its policy is to feature a wide variety of research areas and it welcomes the submission of papers from all parts of the world. Selection for publication is on the basis of reports from specialist referees commissioned by the Editors.