caa a22 4500 445884304 CHVBK 20180317145554.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s10711-010-9526-3 doi (NATIONALLICENCE)springer-10.1007/s10711-010-9526-3 Schaffhauser Florent IHES, 35 route de Chartres, 91440, Bures-sur-Yvette, France aut Moduli spaces of vector bundles over a Klein surface [Elektronische Daten] [Florent Schaffhauser] A compact topological surface S, possibly non-orientable and with non-empty boundary, always admits a Klein surface structure (an atlas whose transition maps are dianalytic). Its complex cover is, by definition, a compact Riemann surface M endowed with an anti-holomorphic involution which determines topologically the original surface S. In this paper, we compare dianalytic vector bundles over S and holomorphic vector bundles over M, devoting special attention to the implications that this has for moduli varieties of semistable vector bundles over M. We construct, starting from S, totally real, totally geodesic, Lagrangian submanifolds of moduli varieties of semistable vector bundles of fixed rank and degree over M. This relates the present work to the constructions of Ho and Liu over non-orientable compact surfaces with empty boundary (Ho and Liu in Commun Anal Geom 16(3):617-679, 2008). Springer Science+Business Media B.V., 2010 Moduli spaces nationallicence Lagrangian submanifolds nationallicence Klein surfaces nationallicence Geometriae Dedicata Springer Netherlands 151/1(2011-04-01), 187-206 0046-5755 151:1<187 2011 151 10711 https://doi.org/10.1007/s10711-010-9526-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10711-010-9526-3 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Schaffhauser Florent IHES, 35 route de Chartres, 91440, Bures-sur-Yvette, France aut NATIONALLICENCE 773 0- Geometriae Dedicata Springer Netherlands 151/1(2011-04-01), 187-206 0046-5755 151:1<187 2011 151 10711 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer