## View abstract

### Session S35 - Moduli Spaces in Algebraic Geometry and Applications

Tuesday, July 20, 18:00 ~ 18:40 UTC-3

## Variations of Hodge Structures of Rank Three $k$-Higgs Bundles and Moduli Spaces of Holomorphic Triples

### Ronald Zúñiga-Rojas

#### Universidad de Costa Rica, Costa Rica   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak9858f9770f29989901ac487d826b1632').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy9858f9770f29989901ac487d826b1632 = 'r&#111;n&#97;ld.z&#117;n&#105;g&#97;r&#111;j&#97;s' + '&#64;'; addy9858f9770f29989901ac487d826b1632 = addy9858f9770f29989901ac487d826b1632 + '&#117;cr' + '&#46;' + '&#97;c' + '&#46;' + 'cr'; var addy_text9858f9770f29989901ac487d826b1632 = 'r&#111;n&#97;ld.z&#117;n&#105;g&#97;r&#111;j&#97;s' + '&#64;' + '&#117;cr' + '&#46;' + '&#97;c' + '&#46;' + 'cr';document.getElementById('cloak9858f9770f29989901ac487d826b1632').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy9858f9770f29989901ac487d826b1632 + '\'>'+addy_text9858f9770f29989901ac487d826b1632+'<\/a>';

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 talk about the cohomology of the critical submanifolds of such moduli spaces, extending those embeddings to moduli spaces of holomorphic triples.