Tangent classes of matroids and wonderful compactifications

• URL: http://arxiv.org/abs/2607.05835v2
• Date: Wed, 08 Jul 2026 14:49:25 GMT
• Title: Tangent classes of matroids and wonderful compactifications
• Abstract summary: We produce an integral tangent class $T_M,mathcalGmathbbZin K_mathbbZ(M,mathcalG)$ in the realizable case.<n>It recovers the Hilbert series of the Chow ring through Hirzebruch--Riemann--Roch, and it satisfies the expected Chern-alpha lower bounds.
• Score: 0.8138288420049126
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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