{"paper":{"title":"A $D$-module approach on the equations of the Rees algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Yairon Cid-Ruiz","submitted_at":"2017-06-19T23:26:09Z","abstract_excerpt":"Let $I \\subset R = \\mathbb{F}[x_1,x_2]$ be a height two ideal minimally generated by three homogeneous polynomials of the same degree $d$, where $\\mathbb{F}$ is a field of characteristic zero. We use the theory of $D$-modules to deduce information about the defining equations of the Rees algebra of $I$. Let $\\mathcal{K}$ be the kernel of the canonical map $\\alpha: \\text{Sym}(I) \\rightarrow \\text{Rees}(I)$ from the symmetric algebra of $I$ onto the Rees algebra of $I$. We prove that $\\mathcal{K}$ can be described as the solution set of a system of differential equations, that the whole bigraded"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.06215","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}