Universal Families on moduli spaces of principal bundles on curves

V. Balaji; I. Biswas; D. S. Nagaraj; P. E. Newstead

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Universal Families on moduli spaces of principal bundles on curves

V. Balaji·I. Biswas·D. S. Nagaraj·P. E. Newstead

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Abstract

Let $H$ be a connected semisimple linear algebraic group defined over $\mathbb C$ and $X$ a compact connected Riemann surface of genus at least three. Let ${\mathcal M}'_X(H)$ be the moduli space parametrising all topologically trivial stable principal $H$-bundles over $X$ whose automorphism group coincides with the centre of $H$. It is a Zariski open dense subset of the moduli space of stable principal $H$-bundles. We prove that there is a universal principal $H$-bundle over $X\times {\mathcal M}'_X(H)$ if and only if $H$ is an adjoint group (that is, the centre of $H$ is trivial).

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BibTeX RIS

V. Balaji, I. Biswas, D. S. Nagaraj, P. E. Newstead. 2006-01-09. Universal Families on moduli spaces of principal bundles on curves. https://arxiv.org/abs/math/0601168

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