提出一种新方法构造拟阵的切类，可复现重要几何性质。
Tangent classes of matroids and wonderful compactifications
- 基于构建集定义拟阵的整数切类，具良好代数性质。
- 在可实现情形下对应美妙紧化空间的切丛类，且满足陈类下界。
- 由AI数学代理独立完成，展示人工智能在数学研究中的潜力。
对于每个无环拟阵 $M$ 及包含顶平坦的 Feichtner--Yuzvinsky 构建集 $/mathcal{G}$，我们构造一个整数切类 $T_{M,/mathcal{G}}^{/mathbb{Z}} \ ext{in } K_{/mathbb{Z}}(M,/mathcal{G})$；在可实现情形下，它退化为相应美妙紧化空间的切丛类，通过 Hirzebruch--Riemann--Roch 公式恢复了 Chow 环的 Hilbert 系列，并满足预期的陈-阿尔法下界。该构造重现了第一作者在 arXiv:2606.22650 中研究的切类及其关键性质。本文主体由 AI 数学推理代理 Danus 自主生成，未受人类数学指导，且在 arXiv:2606.22650 公开前即已解决该问题，展示了 AI 代理在数学研究中的潜力。我们忠实复现其输出，仅添加编辑注释；实验详情见附录 B。
原文摘要 · Abstract (English)
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.
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