Hodge structures of the moduli spaces of pairs
| dc.creator | Muñoz, Vicente | |
| dc.date | 2009-04-12 | |
| dc.date.accessioned | 2026-07-07T13:03:19Z | |
| dc.date.available | 2026-07-07T13:03:19Z | |
| dc.description | Let $X$ be a smooth projective curve of genus $g\geq 2$ over the complex numbers. Fix $n\geq 2$, and an integer $d$. A pair $(E,ϕ)$ over $X$ consists of an algebraic vector bundle $E$ of rank $n$ and degree $d$ over $X$ and a section $ϕ$. There is a concept of stability for pairs which depends on a real parameter $τ$. Let $M_τ(n,d)$ be the moduli space of $τ$-semistable pairs of rank $n$ and degree $d$ over $X$. We prove that the cohomology groups of $M_τ(n,d)$ are Hodge structures isomorphic to direct summands of tensor products of the Hodge structure $H^1(X)$. This implies a similar result for the moduli spaces of stable vector bundles over $X$. | |
| dc.description | 23 pages | |
| dc.identifier | https://arxiv.org/abs/0904.1842 | |
| dc.identifier | http://arxiv.org/abs/0904.1842 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/226758 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14D20;14H60; 14F45 | |
| dc.title | Hodge structures of the moduli spaces of pairs | |
| dc.type | text |