Motivic decompositions of moduli spaces of vector bundles on curves

Abstract

Let $r\ge 2,d$ be two integers which are coprime to each other. Let $C$ be a smooth projective curve of genus $g\ge 2$ and $M(r,L)$ be the moduli space of rank $r$ stable vector bundles on $C$ whose determinants are isomorphic to a fixed line bundle $L$ of degree $d$ on $C.$ In this paper, we study motivic decomposition of $M(r,L)$ for $r=2,3$ cases. We give a new proof of a version of the main result of arXiv:1806.11101. We also found a new motivic decomposition of $M(3,L).$

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