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# The Mukai Pairing and Integral Transforms in Hochschild Homology

@inproceedings{RAMADOSS2008TheMP, title={The Mukai Pairing and Integral Transforms in Hochschild Homology}, author={AJAY C. RAMADOSS}, year={2008} }

- Published 2008

Let X be a smooth proper scheme over a field of characteristic 0. Following Shklyarov [10] , we construct a (non-degenerate) pairing on the Hochschild homology of perf (X), and hence, on the Hochschild homology of X . On the other hand the Hochschild homology of X also has the Mukai pairing (see [1]). If X is Calabi-Yau, this pairing arises from the action of the class of a genus 0 Riemann-surface with two incoming closed boundaries and no outgoing boundary in H0(M0(2, 0)) on the algebra of… CONTINUE READING