Remarks on motives of moduli spaces of rank 2 vector bundles on curves

Abstract

Let $C$ be an algebraic curve of genus $g\ge 2$ and $M_L$ be the moduli space of rank 2 stable vector bundles on $C$ whose determinants are isomorphic to a fixed line bundle $L$ of degree 1 on $C.$ S. del Bano studied motives of moduli spaces of rank 2 vector bundles on $C$ and computed the motive of $M_L.$ In this note, we prove that his result gives an interesting decomposition of the motive of $M_L.$ This motivic decomposition is compatible with a conjecture of M. S. Narasimhan which predicts semi-orthogonal decomposition of derived category of the moduli space.

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References in corpus (1)

• Semiorthogonal decomposition for algebraic varieties

Cited by in corpus (5)

• Motivic decompositions of moduli spaces of vector bundles on curves
• Decompositions of moduli spaces of vector bundles and graph potentials
• Simplification of $\lambda$-ring expressions in the Grothendieck ring of Chow motives
• Semiorthogonal decomposition of ${\mathrm{D}}^b({\mathrm{Bun}}_2^L)$
• Positivity of the Poincaré bundle on the moduli space of vector bundles and its applications