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A formula for the first Chern class of the Verlinde bundle over the modulispace of smooth genus g curves is given. A finite-dimensional argument ispresented in rank 2 using geometric symmetries obtained from strange duality,relative Serre duality, and Wirtinger duality together with the projectiveflatness of the Hitchin connection. A derivation using conformal-block methodsis presented in higher rank. An expression for the first Chern class over thecompact moduli space of curves is obtained.

The Chern classes of the Verlinde bundles