{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T15:31:21Z","timestamp":1759073481975},"reference-count":27,"publisher":"World Scientific Pub Co Pte Lt","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Math."],"published-print":{"date-parts":[[2012,8]]},"abstract":"<jats:p> Let G be a reductive affine algebraic group and let X be an affine algebraic G-variety. We establish a (poly)stability criterion for points x \u2208 X in terms of intrinsically defined closed subgroups H<jats:sub>x<\/jats:sub> of G and relate it with the numerical criterion of Mumford and with Richardson and Bate\u2013Martin\u2013R\u00f6hrle criteria, in the case X = G<jats:sup>N<\/jats:sup>. Our criterion builds on a close analogue of a theorem of Mundet and Schmitt on polystability and allows the generalization to the algebraic group setting of results of Johnson\u2013Millson and Sikora about complex representation varieties of finitely presented groups. By well established results, it also provides a restatement of the non-abelian Hodge theorem in terms of stability notions. <\/jats:p>","DOI":"10.1142\/s0129167x12500826","type":"journal-article","created":{"date-parts":[[2012,3,23]],"date-time":"2012-03-23T15:22:12Z","timestamp":1332516132000},"page":"1250082","source":"Crossref","is-referenced-by-count":5,"title":["STABILITY OF AFFINE G-VARIETIES AND IRREDUCIBILITY IN REDUCTIVE GROUPS"],"prefix":"10.1142","volume":"23","author":[{"given":"CARLOS","family":"FLORENTINO","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica, Instituto Superior T\u00e9cnico, Univ. T\u00e9cnica de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal"}]},{"given":"ANA CRISTINA","family":"CASIMIRO","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Faculdade de Ci\u00eancias e Tecnologia, Univ. Nova de Lisboa, Quinta da Torre 2829-516 Caparica, Portugal"}]}],"member":"219","published-online":{"date-parts":[[2012,7,10]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/s00222-004-0425-9"},{"key":"rf2","first-page":"213","volume":"621","author":"Bate M.","journal-title":"J. Reine Angew. Math."},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.2307\/1970884"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0941-6"},{"key":"rf6","doi-asserted-by":"crossref","first-page":"361","DOI":"10.4310\/jdg\/1214442469","volume":"28","author":"Corlette K.","journal-title":"J. Differential Geom."},{"key":"rf7","first-page":"127","volume":"55","author":"Donaldson S. K.","journal-title":"Proc. London Math. Soc. 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