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https://www.ias.ac.in/article/fulltext/pmsc/126/04/0557-0575

Orbifolds; polystable vector bundle; fundamental group; unitary representation

Let $X$ be a smooth complex projective variety of dimension $n$ and $\mathcal{L}$ an ample line bundle on it. There is a well known bijective correspondence between the isomorphism classes of polystable vector bundles $E$ on $X$ with $c_{1}(E) = 0 = c_{2}(E) \cdot c_{1} \mathcal (L)^{n−2}$ and the equivalence classes of unitary representations of $\pi_{1}(X)$. We show that this bijective correspondence extends to smooth orbifolds.

INDRANIL BISWAS AMIT HOGADI

Published

25 October 2016

Manuscript received

28 October 2014

Manuscript revised

Accepted

5 March 2015

Early published

Unedited version published online

Final version published online

25 October 2016