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Let $X$ be a smooth projective variety over $\mathbb{C}$. The following information is all equivalent (any of these numbers can be computed by a linear equation from any of the others): the ...

I'm confused with working out the Chern character in the following special setting. Let $E$ be a spinor bundle $$S=P_{Spin(2n)}(S^{2n})\times_\rho \mathbb{C}^{2n}$$ over sphere $S^{2n}$, where $\rho$ ...