Abstract
There is an isomorphism between the moduli spaces of \(\sigma \)-stable holomorphic triples and some of the critical submanifolds of the moduli space of k-Higgs bundles of rank three, whose elements \((E,\varphi ^k)\) correspond to variations of Hodge structure, VHS. There are special embeddings on the moduli spaces of k-Higgs bundles of rank three. The main objective here is to study the cohomology of the critical submanifolds of such moduli spaces, extending those embeddings to moduli spaces of holomorphic triples.
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Acknowledgements
I would like to thank Peter B. Gothen for introducing me to the beautiful subject of Higgs bundles. I thank Vicente Muñoz and André Gamma Oliveira for enlightening discussions about the moduli space of triples; I thank Steven Bradlow too, for the time and discussions about stable pairs and triples. I am grateful to Joseph C. Várilly for helpful discussions. Financial support from Fundação para a Ciência e a Tecnologia (FCT), and from Vicerrectoría de Investigación de la Universidad de Costa Rica, is acknowledged.
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Supported by Universidad de Costa Rica through Escuela de Matemática, specifically through CIMM (Centro de Investigaciones Matemáticas y Metamatemáticas), Project 820-B8-224. This work is partly based on the Ph.D. Project [29] called “Homotopy Groups of the Moduli Space of Higgs Bundles”, supported by FEDER through Programa Operacional Factores de Competitividade-COMPETE, and also supported by FCT (Fundação para a Ciência e a Tecnologia) through the Projects PTDC/MAT-GEO/0675/2012 and PEst-C/MAT/UI0144/2013 with Grant Reference SFRH/BD/51174/2010.
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Zúñiga-Rojas, R.A. Variations of hodge structures of rank three k-Higgs bundles and moduli spaces of holomorphic triples. Geom Dedicata 213, 137–172 (2021). https://doi.org/10.1007/s10711-020-00572-0
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DOI: https://doi.org/10.1007/s10711-020-00572-0