{"corpus_id":50186548,"paper_sha":"5cd05bff3661362744ce5af43ec555467bf2becf","doi":"10.4171/PM/1977","arxiv_id":"1408.2105","pmid":null,"pmcid":null,"mag_id":2249001036,"dblp_id":null,"acl_id":null,"title":"Computations and Equations for Segre-Grassmann hypersurfaces","year":2014,"publication_date":"2014-08-09","venue":"","journal":{"name":"arXiv: Algebraic Geometry","pages":null,"volume":""},"journal_issn":null,"journal_title":null,"publication_types":[],"pubmed_pub_types":null,"s2_fields_of_study":["Mathematics"],"reference_count":52,"citation_count":7,"influential_citation_count":0,"is_open_access":true,"arxiv_categories":["math.AG"],"arxiv_license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","arxiv_journal_ref":"Portugaliae Mathematica Vol. 73, Fasc. 1, 2016, 71-90","mesh_headings":null,"chemicals":null,"comments_corrections":null,"source_flags":1,"s2_open_access_pdf_url":"https://arxiv.org/pdf/1408.2105","s2_open_access_landing_url":"https://www.semanticscholar.org/paper/5cd05bff3661362744ce5af43ec555467bf2becf","s2_open_access_license":null,"s2_open_access_status":"GREEN","pmc_open_access_pdf_url":null,"pmc_open_access_landing_url":null,"pmc_open_access_license":null,"pmc_open_access_status":null,"unpaywall_open_access_pdf_url":null,"unpaywall_open_access_landing_url":null,"unpaywall_open_access_license":null,"unpaywall_open_access_status":null,"abstract":"In 2013, Abo and Wan studied the analogue of Waring's problem for systems of skew-symmetric forms and identified several defective systems. Of particular interest is when a certain secant variety of a Segre-Grassmann variety is expected to fill the natural ambient space, but is actually a hypersurface. Algorithms implemented in Bertini are used to determine the degrees of several of these hypersurfaces, and representation-theoretic descriptions of their equations are given. We answer Problem 6.5 [Abo-Wan2013], and confirm their speculation that each member of an infinite family of hypersurfaces is minimally defined by a (known) determinantal equation. While led by numerical evidence, we provide non-numerical proofs for all of our results.","claims":[{"public_id":"cl_6ad52aaf071d37ad01dde86c99e7954b","status":"active","text":"All stated results are proved by non-numerical arguments despite being guided by numerical evidence.","confidence":0.93,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/claims/cl_6ad52aaf071d37ad01dde86c99e7954b"},{"public_id":"cl_e1c3d7c9ac1bd5c7d78fd5bbf79794af","status":"active","text":"Degrees of several Segre-Grassmann hypersurfaces are determined using algorithms implemented in Bertini.","confidence":0.97,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/claims/cl_e1c3d7c9ac1bd5c7d78fd5bbf79794af"},{"public_id":"cl_a30fbb7083742a08f35817a836c93be3","status":"active","text":"Each member of the infinite family of hypersurfaces is minimally defined by a known determinantal equation.","confidence":0.96,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/claims/cl_a30fbb7083742a08f35817a836c93be3"},{"public_id":"cl_5bd67c531f2e971f3184122b77948757","status":"active","text":"Problem 6.5 from Abo and Wan is answered.","confidence":0.98,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous 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