Theta Functions for $\SL(n)$ versus $\GL(n)$
| dc.creator | Donagi, Ron | |
| dc.creator | Tu, Loring W. | |
| dc.date | 1993-03-28 | |
| dc.date.accessioned | 2026-07-07T09:05:48Z | |
| dc.date.available | 2026-07-07T09:05:48Z | |
| dc.description | Over a smooth complex projective curve $C$ of genus $g$ let $\M (n,d)$ be the moduli space of semistable bundles of rank $n$ and degree $d$ on $C$, and $\SM (n,L)$, the moduli space of those bundles whose determinant is isomorphic to a fixed line bundle $L$ over $C$. Let $θ_F$ and $θ$ be theta bundles over these two moduli spaces. We prove a simple formula relating their spaces of sections: if $h=\gcd (n,d)$ is the greatest common divisor of $n$ and $d$, and $L\in \Pic ^d(C)$, then $$\dim H^0(\SM (n,L), θ^k) \cdot k^g=\dim H^0(\M(n,d),θ_F^k)\cdot h^g.$$ We also formulate a conjectural duality between these two types of spaces of sections. | |
| dc.description | 10 pages, Latex | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9303004 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9303004 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/149801 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Theta Functions for $\SL(n)$ versus $\GL(n)$ | |
| dc.type | text |