scholarly journals Intersection Theory on Moduli Spaces of Holomorphic Bundles of Arbitrary Rank on a Riemann Surface

1998 ◽  
Vol 148 (1) ◽  
pp. 109 ◽  
Author(s):  
Lisa C. Jeffrey ◽  
Frances C. Kirwan
Keyword(s):  
Riemann Surface ◽  
Moduli Spaces ◽  
Intersection Theory ◽  
Arbitrary Rank ◽  
Holomorphic Bundles

scholarly journals Representations with Weighted Frames and Framed Parabolic Bundles

2000 ◽  
Vol 52 (6) ◽  
pp. 1235-1268 ◽  
Author(s):  
J. C. Hurtubise ◽  
L. C. Jeffrey
Keyword(s):  
Riemann Surface ◽  
Fundamental Group ◽  
Moduli Spaces ◽  
Symplectic Reduction ◽  
Toric Geometry ◽  
Parabolic Bundles ◽  
Parabolic Structure ◽  
Complex Variety ◽  
Holomorphic Bundles ◽  
Connected Lie Group

AbstractThere is a well-known correspondence (due to Mehta and Seshadri in the unitary case, and extended by Bhosle and Ramanathan to other groups), between the symplectic variety Mh of representations of the fundamental group of a punctured Riemann surface into a compact connected Lie group G, with fixed conjugacy classes h at the punctures, and a complex variety of holomorphic bundles on the unpunctured surface with a parabolic structure at the puncture points. For G = SU(2), we build a symplectic variety P of pairs (representations of the fundamental group into G, “weighted frame” at the puncture points), and a corresponding complex variety of moduli of “framed parabolic bundles”, which encompass respectively all of the spaces Mh, , in the sense that one can obtain Mh from P by symplectic reduction, andMh from by a complex quotient. This allows us to explain certain features of the toric geometry of the SU(2) moduli spaces discussed by Jeffrey and Weitsman, by giving the actual toric variety associated with their integrable system.

scholarly journals Correction to: Masur–Veech volumes and intersection theory on moduli spaces of Abelian differentials

2021 ◽  
Author(s):  
Dawei Chen ◽  
Martin Möller ◽  
Adrien Sauvaget ◽  
Don Zagier
Keyword(s):  
Moduli Spaces ◽  
Intersection Theory ◽  
Abelian Differentials

A Correction to this paper has been published: https://doi.org/10.1007/s00222-020-00969-4

scholarly journals Intersection pairings on singular moduli spaces of bundles over a Riemann surface and their partial desingularisations

2006 ◽  
Vol 11 (3) ◽  
pp. 439-494
Author(s):  
Lisa Jeffrey ◽  
Young-Hoon Kiem ◽  
Frances C. Kirwan ◽  
Jonathan Woolf
Keyword(s):  
Riemann Surface ◽  
Moduli Spaces ◽  
Singular Moduli

scholarly journals CHEN–RUAN COHOMOLOGY OF SOME MODULI SPACES, II

2010 ◽  
Vol 21 (04) ◽  
pp. 497-522 ◽  
Author(s):  
INDRANIL BISWAS ◽  
MAINAK PODDAR
Keyword(s):  
Riemann Surface ◽  
Line Bundle ◽  
Prime Number ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Vector Bundles ◽  
Line Bundles ◽  
Holomorphic Line Bundle ◽  
Stable Vector Bundles

Let X be a compact connected Riemann surface of genus at least two. Let r be a prime number and ξ → X a holomorphic line bundle such that r is not a divisor of degree ξ. Let [Formula: see text] denote the moduli space of stable vector bundles over X of rank r and determinant ξ. By Γ we will denote the group of line bundles L over X such that L⊗r is trivial. This group Γ acts on [Formula: see text] by the rule (E, L) ↦ E ⊗ L. We compute the Chen–Ruan cohomology of the corresponding orbifold.

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