Abstract
Let X be an irreducible smooth projective curve, of genus at least two, over an algebraically closed field k. Let 
denote the moduli stack of principal G-bundles over X of fixed topological type \(d \in \pi _1(G)\), where G is any almost simple affine algebraic group over k. We prove that the universal bundle over 
is stable with respect to any polarization on 
. A similar result is proved for the Poincaré adjoint bundle over \(X \,{\times }\, M_G^{d, {\mathrm {rs}}}\), where \(M_G^{d, {\mathrm {rs}}}\) is the coarse moduli space of regularly stable principal G-bundles over X of fixed topological type d.
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Indranil Biswas is supported by a J. C. Bose Fellowship. Tomás L. Gómez acknowledges funding from the Spanish MINECO (Grant MTM2016-79400-P and ICMAT Severo Ochoa Project SEV-2015-0554) and the 7th European Union Framework Programme (Marie Curie IRSES Grant 612534 Project MODULI) and CSIC (2019AEP151 and Ayuda extraordinaria a Centros de Excelencia Severo Ochoa 20205CEX001). Norbert Hoffmann was supported by Mary Immaculate College Limerick through the PLOA sabbatical programme. He thanks the Tata Institute of Fundamental Research in Bombay for its hospitality.
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Biswas, I., Gómez, T.L. & Hoffmann, N. Stability of the Poincaré bundle. European Journal of Mathematics 7, 633–640 (2021). https://doi.org/10.1007/s40879-020-00444-7
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DOI: https://doi.org/10.1007/s40879-020-00444-7