1995/05/24 by Indranil Biswas, Biswas, Indranil, Subhashis Nag +3
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #FOS: Physical sciences #Geometric and Algebraic Topology #Geometry and complex manifolds #High Energy Physics - Theory (hep-th)
paper · pdf · doi:10.48550/arxiv.alg-geom/9505024
openalex publication_date 1995/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
There exists on each Teichmüller space Tg (comprising compact Riemann surfaces of genus g), a natural sequence of determinant (of cohomology) line bundles, DETn, related to each other via certain ``Mumford isomorphisms''. There is a remarkable connection, (Belavin-Knizhnik), between the Mumford isomorphisms and the existence of the Polyakov string measure on the Teichmüller space. This suggests the question of finding a genus-independent formulation of these bundles and their isomorphisms. In this paper we combine a Grothendieck-Riemann-Roch lemma with a new concept of C* ⊗ Q bundles to construct such an universal version. Our universal objects exist over the universal space, T_∞, which is the direct limit of the Tg as the genus varies over the tower of all unbranched coverings of any base surface. The bundles and the connecting isomorphisms are equivariant with respect to the natural action of the universal commensurability modular group.