RT Journal Article
T1 The Torelli theorem for the moduli spaces of connections on a Riemann surface
A1 Biswas, Indranil
A1 Muñoz, Vicente
AB Let (X, x0) be any one-pointed compact connected Riemann surface of genus g, with g > 3. Fix two mutually coprime integers r > 1 and d. LetMX denote the moduli space parametrizing all logarithmic SL(r,C)-connections, singular over x0, on vector bundles over X of degree d. We prove that the isomorphism class of the variety MX determines the Riemann surface X uniquely up to an isomorphism, although the biholomorphism class of MX is known to be independent of the complex structure of X. The isomorphism class of the variety MX is independent of the point x0 2 X. A similar result is proved for the moduli space parametrizing logarithmic GL(r,C)-connections, singular over x0, on vector bundles over X of degree d. The assumption r > 1 is necessary for the moduli space of logarithmic GL(r,C)-connections to determine the isomorphism class of X uniquely.
PB Elsevier Science
SN 0166-8641
YR 2007
FD 2007
LK https://hdl.handle.net/20.500.14352/50602
UL https://hdl.handle.net/20.500.14352/50602
LA eng
NO MEC
DS Docta Complutense
RD 10 abr 2025