Corpus ID: 237532215

Branched SL(r,C)-opers

@inproceedings{Biswas2021BranchedS,
  title={Branched SL(r,C)-opers},
  author={Indranil Biswas and Sorin Dumitrescu and Sebastian Heller},
  year={2021}
}
Branched projective structures were introduced by Mandelbaum [21], [22], and opers were introduced by Beilinson and Drinfeld [2], [3]. We define the branched analog of SL(r,C)–opers and investigate their properties. For the usual SL(r,C)–opers, the underlying holomorphic vector bundle is independent of the opers. For the branched SL(r,C)–opers, the underlying holomorphic vector bundle actually depends on the oper. Given a branched SL(r,C)–oper, we associate to it another holomorphic vector… Expand

References

SHOWING 1-10 OF 31 REFERENCES
BRANCHED PROJECTIVE STRUCTURES, BRANCHED SO(3, C)-OPERS AND LOGARITHMIC CONNECTIONS ON JET BUNDLE
We study the branched holomorphic projective structures on a compact Rie-mann surface X with a fixed branching divisor S = d i=1 x i , where x i ∈ X are distinct points. After defining branched SO(3,Expand
Generalized B-Opers
Opers were introduced by Beilinson-Drinfeld [arXiv:math.AG/0501398]. In [J. Math. Pures Appl. 82 (2003), 1-42] a higher rank analog was considered, where the successive quotients of the operExpand
Branched holomorphic Cartan geometries and Calabi-Yau manifolds
We introduce the concept of a branched holomorphic Cartan geometry. It generalizes to higher dimension the definition of branched (flat) complex projective structure on a Riemann surface introducedExpand
Branched structures on Riemann surfaces
Following results of Gunning on geometric realizations of projective structures on Riemann surfaces, we investigate more fully certain generalizations of such structures. We define the notion of aExpand
On the relations between branched structures and affine and projective bundles on Riemann surfaces
A classification for analytic branched G-structures on a Riemann surface M is provided by means of a map (G into the moduli spaces of flat G-bundles on M. (G = GA(1, C) or PL(1, C).) Conditions areExpand
Spectral curves, opers and integrable systems
We establish a general link between integrable systems in algebraic geometry (expressed as Jacobian flows on spectral curves) and soliton equations (expressed as evolution equations on flatExpand
Complex analytic connections in fibre bundles
Introduction. In the theory of differentiable fibre bundles, with a Lie group as structure group, the notion of a connection plays an important role. In this paper we shall consider complex analyticExpand
On Uniformization of Complex Manifolds: The Role of Connections
TLDR
The classical uniformization theorem for Riemann surfaces and its recent extensions can be viewed as introducing special pseudogroup structures, affine or projective structures, on higher-dimensional complex manifolds, modeled on the theory as developed for R Siemann surfaces. Expand
Weyl modules and opers without monodromy
We prove that the algebra of endomorphisms of a Weyl module of critical level is isomorphic to the algebra of functions on the space of monodromy-free opers on the disc with regular singularity andExpand
Gaudin Model and Opers
This is a review of our previous works [FFR, F1, F3] (some of them joint with B. Feigin and N. Reshetikhin) on the Gaudin model and opers. We define a commutative subalgebra in the tensor power ofExpand
...
1
2
3
4
...