Articles written in Proceedings – Mathematical Sciences

    • On Harder-Narasimhan reductions for Higgs principal bundles

      Arijit Dey R Parthasarathi

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      The existence and uniqueness of H-N reduction for the Higgs principal bundles over nonsingular projective variety is shown. We also extend the notion of H-N reduction for (Γ,G)-bundles and ramifiedG-bundles over a smooth curve.

    • On stability of tangent bundle of toric varieties


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      Let $X$ be a nonsingular complex projective toric variety. We address the question of semi-stability as well as stability for the tangent bundle $TX$. In particular, a complete answer is given when $X$ is a Fano toric variety of dimension four with Picard number at most two, complementing the earlier work of Nakagawa (Tohoku. Math. J. 45 (1993) 297--310; 46 (1994) 125--133). We also give an infinite set of examples of Fano toric varieties for which $TX$ is unstable; the dimensions of this collection of varieties are unbounded. Our method is based on the equivariant approach initiated by Klyachko (Izv. Akad. Nauk. SSSR Ser. Mat. 53 (1989) 1001--1039, 1135) and developed further by Perling (Math. Nachr. 263/264 (2004) 181--197) and Kool (Moduli spaces of sheaves on toric varieties, Ph.D. thesis (2010) (University of Oxford); Adv. Math. 227 (2011) 1700--1755).

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