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Revista de Matemática Teoría y Aplicaciones

versión impresa ISSN 1409-2433

Rev. Mat vol.28 no.1 San José ene./jul. 2021 


Notes on coherent systems

Notas sobre los sistemas coherentes

Alexander H.W. Schmitt1 

1Freie Universität Berlin; Institut für Mathematik; Arnimallee 3; D-14195 Berlin, Germany;


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.

Keywords: coherent system; moduli space; Hitchin map; first fundamental theorem of invariant theory.


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.

Palabras clave: sistema coherente; espacio de móduli; morfismo de Hitchin; primer teorema fundamental de la teoría de invariantes.

Mathematics Subject Classification: 14H40, 14D20, 13A50.

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Leticia Brambila-Paz brought the problem of studying coherent Higgs systems to my attention. It was formulated by Bradlow, Brambila-Paz, García-Prada, and Gothen and served as starting point for [34] and this note. Bradlow, BrambilaPaz, García-Prada, and Gothen and Brambila-Paz and Edgar I. Castañeda-González are carrying out independent research on the case of coherent Higgs systems. Their results will appear in forthcoming papers. I thank Peter Newstead for the references [14] and [38] and Ángel Muñoz Castañeda for the translation of the title and the abstract into Spanish. I am also grateful to Luisa González Campos and Ronald Zuñiga Rojas for their hospitality during my visit to Costa Rica for the XXII SIMMAC.


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Received: June 02, 2020; Revised: November 04, 2020; Accepted: November 12, 2020

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