{"paper":{"title":"A Kronecker algorithm for locally closed sets over a perfect field","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.SC"],"primary_cat":"math.AG","authors_text":"Guillermo Matera, Joos Heintz, Luis Miguel Pardo, Mariana P\\'erez, Melina Privitelli, Nardo Gim\\'enez","submitted_at":"2025-12-16T20:11:59Z","abstract_excerpt":"We develop a probabilistic algorithm of Kronecker type for computing a Kronecker representation of a zero-dimensional linear section of an algebraic variety $V$ defined over a perfect field $k$. The variety $V$ is the Zariski closure of the set of common zeros $\\{F_1=0,\\ldots,F_r=0,G\\not=0\\}$ of multivariate polynomials $F_1,\\ldots,F_r\\in k[X_1,\\ldots,X_n]$ outside a prescribed hypersurface $\\{G=0\\}$. We assume that $F_1,\\ldots,F_r$ satisfy natural geometric conditions, such as regularity and radicality, in the local ring $k[X_1,\\ldots,X_n]_G$. Our approach combines homotopic deformation techn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.14888","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2512.14888/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}