Tangent classes of matroids and wonderful compactifications
For mathematicians studying matroids and wonderful compactifications, this provides a new construction and demonstrates AI's potential in mathematical research, though the mathematical contribution is incremental as it reproduces known results.
The paper constructs an integral tangent class for loopless matroids with Feichtner-Yuzvinsky building sets, which specializes to the tangent bundle of wonderful compactifications in the realizable case and satisfies key properties like Chern-alpha lower bounds. The work was produced autonomously by an AI agent, Danus, before a related human preprint was available.
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.