
TL;DR
This paper introduces polarized real tori, showing their parametrization by a convex cone and relating their line bundles to those on associated real abelian varieties, thus establishing a moduli space framework.
Contribution
It defines polarized real tori, connects them to the convex cone ${ m f P}_g$, and constructs a moduli space using Minkowski domain, linking line bundles to real abelian varieties.
Findings
${ m f P}_g$ parametrizes principally polarized real tori.
The Minkowski domain ${ m f R}_g$ serves as a moduli space.
Line bundles on real tori relate to holomorphic line bundles on abelian varieties.
Abstract
For a fixed positive integer , we let be the open convex cone in the Euclidean space . Then the general linear group acts naturally on by (). We introduce a notion of polarized real tori. We show that the open cone parametrizes principally polarized real tori of dimension and that the Minkowski domain may be regarded as a moduli space of principally polarized real tori of dimension . 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.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic Geometry and Number Theory · Geometry and complex manifolds
