<?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>S1409-24332021000100001</article-id>
<article-id pub-id-type="doi">10.15517/rmta.v28i1.42154</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Notes on coherent systems]]></article-title>
<article-title xml:lang="es"><![CDATA[Notas sobre los sistemas coherentes]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Schmitt]]></surname>
<given-names><![CDATA[Alexander H.W.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Freie Universität Berlin  Institut für Mathematik]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Germany</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>07</month>
<year>2021</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>07</month>
<year>2021</year>
</pub-date>
<volume>28</volume>
<numero>1</numero>
<fpage>1</fpage>
<lpage>38</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S1409-24332021000100001&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S1409-24332021000100001&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S1409-24332021000100001&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract We present an alternative approach to semistability and moduli spaces for coherent systems associated with decorated vector bundles. In this approach, it seems possible to construct a Hitchin map. We relate some examples to classical problems from geometric invariant theory.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen En estas notas se presenta un nuevo enfoque para el estudio de las condiciones de semi-estabilidad, así como de los espacios de móduli, de los sistemas coherentes asociados a fibrados vectoriales con estructura adicional. Bajo este enfoque, se abre la posibilidad de definir un morfismo de Hitchin. Se muestra, además, la relación entre algunos ejemplos concretos con problemas clásicos presentes en la teoría geométrica de invariantes.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[coherent system]]></kwd>
<kwd lng="en"><![CDATA[moduli space]]></kwd>
<kwd lng="en"><![CDATA[Hitchin map]]></kwd>
<kwd lng="en"><![CDATA[first fundamental theorem of invariant theory.]]></kwd>
<kwd lng="es"><![CDATA[sistema coherente]]></kwd>
<kwd lng="es"><![CDATA[espacio de móduli]]></kwd>
<kwd lng="es"><![CDATA[morfismo de Hitchin]]></kwd>
<kwd lng="es"><![CDATA[primer teorema fundamental de la teoría de invariantes.]]></kwd>
</kwd-group>
</article-meta>
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