Hitchin systems on singular curves II. Gluing subschemes
| dc.creator | Chervov, A. | |
| dc.creator | Talalaev, D. | |
| dc.date | 2003-09-04 | |
| dc.date | 2003-09-10 | |
| dc.date.accessioned | 2026-07-07T10:49:44Z | |
| dc.date.available | 2026-07-07T10:49:44Z | |
| dc.description | In this paper we continue our studies of Hitchin systems on singular curves (started in hep-th/0303069). We consider a rather general class of curves which can be obtained from the projective line by gluing two subschemes together (i.e. their affine part is: Spec $\{f \in \CC[z]: f(A(\ep))=f((B(\ep)); \ep^N=0 \}$, where $A(\ep), B(\ep)$ are arbitrary polynomials) . The most simple examples are the generalized cusp curves which are projectivizations of Spec $\{f \in \CC[z]: f'(0)=f''(0)=...f^{N-1}(0)=0 \}$). We describe the geometry of such curves; in particular we calculate their genus (for some curves the calculation appears to be related with the iteration of polynomials $A(\ep), B(\ep)$ defining the subschemes). We obtain the explicit description of moduli space of vector bundles, the dualizing sheaf, Higgs field and other ingredients of the Hitchin integrable systems; these results may deserve the independent interest. We prove the integrability of Hitchin systems on such curves. To do this we develop $r$-matrix formalism for the functions on the truncated loop group $GL_n(\CC[z]), z^N=0$. We also show how to obtain the Hitchin integrable systems on such curves as hamiltonian reduction from the more simple system on some finite-dimensional space. | |
| dc.description | 36 pages | |
| dc.identifier | https://arxiv.org/abs/hep-th/0309059 | |
| dc.identifier | http://arxiv.org/abs/hep-th/0309059 | |
| dc.identifier | Int.J.Geom.Meth.Mod.Phys.4:751-787,2007 | |
| dc.identifier | doi:10.1142/S0219887807002284 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/184319 | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Mathematical Physics | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.title | Hitchin systems on singular curves II. Gluing subschemes | |
| dc.type | text |