<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>1409-2433</journal-id>
<journal-title><![CDATA[Revista de Matemática Teoría y Aplicaciones]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. Mat]]></abbrev-journal-title>
<issn>1409-2433</issn>
<publisher>
<publisher-name><![CDATA[Centro de Investigaciones en Matemática Pura y Aplicada (CIMPA) y Escuela de Matemática, San José, Costa Rica.]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1409-24332019000200197</article-id>
<article-id pub-id-type="doi">10.15517/rmta.v26i2.38315</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[A brief survey of higgs bundles]]></article-title>
<article-title xml:lang="es"><![CDATA[Un estudio conciso de fibrados de higgs]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Zúñiga-Rojas]]></surname>
<given-names><![CDATA[Ronald A.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad de Costa Rica Escuela de Matemática Centro de Investigaciones Matemáticas y Metamatemáticas CIMM]]></institution>
<addr-line><![CDATA[ San José]]></addr-line>
<country>Costa Rica</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2019</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2019</year>
</pub-date>
<volume>26</volume>
<numero>2</numero>
<fpage>197</fpage>
<lpage>214</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S1409-24332019000200197&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S1409-24332019000200197&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S1409-24332019000200197&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract Considering a compact Riemann surface of genus greater or equal than two, a Higgs bundle is a pair composed of a holomorphic bundle over the Riemann surface, joint with an auxiliar vector field, so-called Higgs field. This theory started around thirty years ago, with Hitchin&#8217;s work, when he reduced the self-duality equations from dimension four to dimension two, and so, studied those equations over Riemann surfaces. Hitchin baptized those fields as Higgs fields because in the context of physics and gauge the- ory, they describe similar particles to those described by the Higgs bosson. Later, Simpson used the name Higgs bundle for a holomorphic bundle to- gether with a Higgs field. Today, Higgs bundles are the subject of research in several areas such as non-abelian Hodge theory, Langlands, mirror sym- metry, integrable systems, quantum field theory (QFT), among others. The main purposes here are to introduce these objects, and to present a brief but complete construction of the moduli space of Higgs bundles.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen Considerando una superficie compacta de Riemann de género mayor o igual que dos, un fibrado de Higgs es un par compuesto por un fibrado holomorfo sobre la superficie de Riemann, junto con un campo vectorial auxiliar, llamado campo de Higgs. Esta teoría inició hace unos treinta años, con el trabajo de Hitchin, cuando él reduce las ecuaciones de auto- dualidad de dimensión cuatro a dimensión dos, y así, estudiar esas ecua- ciones sobre superficies de Riemann. Hitchin bautizó esos campos como campos de Higgs pues en el contexto de la física y de la teoría de gauge, describen partículas similares a las descritas por el bozón de Higgs. Más tarde, Simpson usó el nombre fibrado de Higgs para un fibrado holomorfo junto con un campo de Higgs. Hoy, los fibrados de Higgs son objeto de investigación en varias áreas tales como la teoría de Hodge no abeliana, Langlands, simetría de espejo, sistemas integrables, teoría cuántica de campos (QFT), entre otros. Los propósitos principales aquí son introducir estos objetos y presentar una breve pero completa construcción del espacio móduli de los fibrados de Higgs y algunas de sus estratificaciones.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Higgs bundles]]></kwd>
<kwd lng="en"><![CDATA[Hodge bundles]]></kwd>
<kwd lng="en"><![CDATA[moduli spaces]]></kwd>
<kwd lng="en"><![CDATA[stable triples]]></kwd>
<kwd lng="en"><![CDATA[vector bundles]]></kwd>
<kwd lng="es"><![CDATA[fibrados de Higgs]]></kwd>
<kwd lng="es"><![CDATA[fibrados de Hodge]]></kwd>
<kwd lng="es"><![CDATA[espacios móduli]]></kwd>
<kwd lng="es"><![CDATA[triples estables]]></kwd>
<kwd lng="es"><![CDATA[fibrados vectoriales]]></kwd>
</kwd-group>
</article-meta>
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