Tangent classes of matroids and wonderful compactifications

Abstract

For every loopless matroid $M$ and every Feichtner--Yuzvinsky building set $\mathcal{G}$ containing the top flat, we construct an integral tangent class $T_{M,\mathcal{G}}^{\mathbb{Z}}\in K_{\mathbb{Z}}(M,\mathcal{G})$; in the realizable case it specializes to the class of the tangent bundle of the corresponding wonderful compactification, it recovers the Hilbert series of the Chow ring through Hirzebruch--Riemann--Roch, and it satisfies the expected Chern-alpha lower bounds. This reproduces the tangent class and its key properties studied by the first author in arXiv:2606.22650. The main body of this paper was produced autonomously, without human mathematical guidance, by Danus, an AI mathematical reasoning agent. Danus solved the problem before arXiv:2606.22650 was publicly available, demonstrating the potential of AI agents in mathematical research. We reproduce its output faithfully, adding only editorial comments; the experiment is documented in Appendix B.

Disclosure

“{M, G}))$ (iii) For $k \leq d$, we have $\deg_{M,\G} (c_k(T_{M,\G}) \alpha^{d-k}) \geq \binom{d+1}{k}$ and prove rigorously that the constructed class satisfies the above properties. Appendix B. Usage of Generative AI Guoxiong Gao and Shurui Liu Except for the abstract and introduction, which were rewritten by the human authors, the main mathematical text, including Sections 4–6, was generated by Danus [Liu+ 26], a m”

PDF page 30

Classification

Substantial mathematical content or result generation

Multiplier

10

Verified

2026-08-24T00:34:09.244Z

Structural counts