Polarized Real Tori

Details Polarized Real Tori Polarized Real Tori

2009-12-28

arxiv.org/abs/0912.5084v2

Mathematics

Algebraic Geometry

58 pages

Scientific paper

For a fixed positive integer $g$, we let ${\mathcal P}_g = \big\{Y\in {\mathbb R}^{(g,g)} | Y= {}^tY>0 \big\}$ be the open convex cone in the Euclidean space ${\mathbb R}^{g(g+1)/2}$. Then the general linear group $GL(g,{\mathbb R})$ acts naturally on ${\mathcal P}_g$ by $A\star Y= AY {}^tA$ ($A\in GL(g,{\mathbb R}), Y\in {\mathcal P}_g$). We introduce a notion of polarized real tori. We show that the open cone ${\mathcal P}_g$ parametrizes principally polarized real tori of dimension $g$ and that the Minkowski domain ${\mathfrak R}_g= GL(g,{\mathbb Z})\backslash {\mathcal P}_g$ may be regarded as a moduli space of principally polarized real tori of dimension $g$. We also study smooth line bundles on a polarized real torus by relating them to holomorphic line bundles on its associated polarized real abelian variety.

Affiliated with

Also associated with

No associations

Rating

Polarized Real Tori 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 Polarized Real Tori, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Polarized Real Tori will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-91442