{"id":91,"date":"2025-06-18T20:58:55","date_gmt":"2025-06-18T19:58:55","guid":{"rendered":"https:\/\/mat.uab.cat\/web\/tfg\/?p=91"},"modified":"2026-02-13T08:17:40","modified_gmt":"2026-02-13T07:17:40","slug":"introduccio-a-la-geometria-algebraica","status":"publish","type":"post","link":"https:\/\/mat.uab.cat\/web\/tfg\/introduccio-a-la-geometria-algebraica\/","title":{"rendered":"Introducci\u00f3 a la geometria algebraica"},"content":{"rendered":"<p>Estem acostumats, en qualsevol espai m\u00e8tric, a poder considerar una bola oberta tan menuda com vullguem. T&#8217;imagines una topologia on tots els oberts s\u00f3n enormes? Potser l&#8217;exemple m\u00e9s fam\u00f3s \u00e9s la topologia de Zariski, la m\u00e9s natural quan considerem conjunts definits com l&#8217;anul\u00b7laci\u00f3 de polinomis (per exemple, el graf d&#8217;una funci\u00f3 polin\u00f2mica o el conjunt de les matrius de determinant $1$). La geometria algebraica \u00e9s la branca de les matem\u00e0tiques encarregada de l&#8217;estudi geom\u00e8tric d&#8217;aquests conjunts a partir de la relaci\u00f3 amb l&#8217;\u00e0lgebra (commutativa). Aquest treball \u00e9s una introducci\u00f3 als principis b\u00e0sics de la geometria algebraica i l&#8217;estudi m\u00e9s detallat d&#8217;un aspecte o exemple representatiu a elecci\u00f3 de l&#8217;estudiant (com, per exemple, els grups algebraics).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Estem acostumats, en qualsevol espai m\u00e8tric, a poder considerar una bola oberta tan menuda com vullguem. T&#8217;imagines una topologia on tots els oberts s\u00f3n enormes? Potser l&#8217;exemple m\u00e9s fam\u00f3s \u00e9s la topologia de Zariski, la m\u00e9s natural quan considerem conjunts definits com l&#8217;anul\u00b7laci\u00f3 de polinomis (per exemple, el graf d&#8217;una funci\u00f3 polin\u00f2mica o el conjunt [&hellip;]<\/p>\n","protected":false},"author":54,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[28,31],"tags":[22],"class_list":["post-91","post","type-post","status-publish","format-standard","hentry","category-algebra","category-geometria-i-topologia","tag-roberto-rubio"],"_links":{"self":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts\/91","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/users\/54"}],"replies":[{"embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/comments?post=91"}],"version-history":[{"count":3,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts\/91\/revisions"}],"predecessor-version":[{"id":639,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts\/91\/revisions\/639"}],"wp:attachment":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/media?parent=91"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/categories?post=91"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/tags?post=91"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}