Torelli theorem for moduli spaces of SL(r,C)-connections on a compact Riemann surface

Details Torelli theorem for moduli spaces of SL(r,C)-connections on a compact Riemann surface Torelli theorem for moduli spaces of SL(r,C)-connections on a compact Riemann surface

2007-02-20

arxiv.org/abs/math/0702579v2

Mathematics

Algebraic Geometry

24 pages, no figures; v2. Final version, accepted in Communications in Contemporary Math

Scientific paper

Let $X$ be any compact connected Riemann surface of genus $g \geq 3$. For any $r\geq 2$, let $M_X$ denote the moduli space of holomorphic $SL(r,C)$-connections over $X$. It is known that the biholomorphism class of the complex variety $M_X$ is independent of the complex structure of $X$. If $g=3$, then we assume that $r\geq 3$. We prove that the isomorphism class of the variety $M_X$ determines the Riemann surface $X$ uniquely up to isomorphism. A similar result is proved for the moduli space of holomorphic $GL(r,C)$-connections on $X$. We also show that the Torelli theorem remains valid for the moduli spaces of connections, as well as those of stable vector bundles, on geometrically irreducible smooth projective curves defined over the field of real numbers.

Affiliated with

Also associated with

No associations

Rating

Torelli theorem for moduli spaces of SL(r,C)-connections on a compact Riemann surface does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Torelli theorem for moduli spaces of SL(r,C)-connections on a compact Riemann surface, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Torelli theorem for moduli spaces of SL(r,C)-connections on a compact Riemann surface will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-383667