{"ID":6023375,"CreatedAt":"2026-07-08T01:00:23.257252134Z","UpdatedAt":"2026-07-10T04:40:34.01444365Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.05835","arxiv_id":"2607.05835","title":"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.","short_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 wonder...","url_abs":"https://arxiv.org/abs/2607.05835","url_pdf":"https://arxiv.org/pdf/2607.05835v1","authors":"[\"Ronnie Cheng\",\"Shurui Liu\",\"Guoxiong Gao\"]","published":"2026-07-07T04:56:22Z","proceeding":"math.AG","tasks":"[\"math.AG\",\"cs.AI\",\"math.CO\"]","methods":"[]","has_code":false}