Determinants of parabolic bundles on Riemann surfaces

Biswas, Indranil; Raghavendra, N.

doi:10.1007/bf02837895

Cited by 19 publications

(23 citation statements)

References 15 publications

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“…In the situation considered in [BR93] the corresponding Laplace operators have no continuous spectrum, and no cuspidal defect appears in this case; the resulting formula is very similar to the original Quillen's one.…”

supporting

confidence: 53%

The first Chern form on moduli of parabolic bundles

Takhtajan

Zograf

2007

Math. Ann.

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Abstract. For moduli space of stable parabolic bundles on a compact Riemann surface, we derive an explicit formula for the curvature of its canonical line bundle with respect to Quillen's metric and interprete it as a local index theorem for the family of∂-operators in the associated parabolic endomorphism bundles. The formula consists of two terms: one standard (proportional to the canonical Kähler form on the moduli space), and one nonstandard, called a cuspidal defect, that is defined by means of special values of the Eisenstein-Maass series. The cuspidal defect is explicitly expressed through the curvature forms of certain natural line bundles on the moduli space related to the parabolic structure. We also compare our result with Witten's volume computation.

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supporting

confidence: 53%

The first Chern form on moduli of parabolic bundles

Takhtajan

Zograf

2007

Math. Ann.

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“…8 We see that the Verlinde number is equal to the dimension of the space of degree k polynomials in d variables, which is consistent with ξ ∼ = O(1) on M P ∼ = P d .…”

Section: Non-abelian Theta Functions On M Pmentioning

confidence: 59%

“…For the map γ in (3.9), the pullback γ * ζ r coincides with the determinant line bundle ζ on M P [7,8]. Therefore, from (3.10) we get an isomorphism…”

Section: Theorem 31 For Any G ∈ (Z/2z) D There Is a Canonical Isommentioning

confidence: 85%

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Quantization of some moduli spaces of parabolic vector bundles on $${{\mathbb C}{\mathbb P}^1}$$

Biswas

Florentino²,

Mourão³

et al. 2012

Ann Glob Anal Geom

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We address quantization of the natural symplectic structure on a moduli space of parabolic vector bundles of parabolic degree zero over CP 1 with four parabolic points and parabolic weights in {0, 1/2}. Identifying such parabolic bundles as vector bundles on an elliptic curve, we obtain explicit expressions for the corresponding non-abelian theta functions. These non-abelian theta functions are described in terms of certain naturally defined distributions on the compact group SU(2).

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“…The group Q acts on A, and it preserves the subset A 8 . The quotient A 8 /Q is M(r,d) [BR,Proposition 3.7].…”

Section: Some Facts About the Moduli Space Of Vector Bundlesmentioning

confidence: 99%