曲线图的动机

IF 1.5 Q2 PHYSICS, MATHEMATICAL
P. Aluffi, M. Marcolli, Waleed Qaisar
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引用次数: 1

摘要

研究了仿射图超曲面补的Grothendieck类的递推关系。我们显式地计算了几个单调图族的这些类,重点关注了与CTKT张量模型相关的具有价-$4$内部顶点的图的情况。结果暗示了一个复杂而有趣的结构,在不同族的图类之间的可除关系或非平凡关系。利用递归关系证明了在模空间$\ mathical M_{0,4}$的类中,所有单调图的Grothendieck类作为多项式是正的。在数百次显式计算的基础上,我们还推测相应的多项式是对数凹的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Motives of melonic graphs
We investigate recursive relations for the Grothendieck classes of the affine graph hypersurface complements of melonic graphs. We compute these classes explicitly for several families of melonic graphs, focusing on the case of graphs with valence-$4$ internal vertices, relevant to CTKT tensor models. The results hint at a complex and interesting structure, in terms of divisibility relations or nontrivial relations between classes of graphs in different families. Using the recursive relations we prove that the Grothendieck classes of all melonic graphs are positive as polynomials in the class of the moduli space $\mathcal M_{0,4}$. We also conjecture that the corresponding polynomials are log-concave, on the basis of hundreds of explicit computations.
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来源期刊
CiteScore
2.30
自引率
0.00%
发文量
16
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