# Determinant bundles and Virasoro algebras

@article{Beilinson1988DeterminantBA, title={Determinant bundles and Virasoro algebras}, author={Alexander Beilinson and Vadim Schechtman}, journal={Communications in Mathematical Physics}, year={1988}, volume={118}, pages={651-701} }

We consider the interplay of infinite-dimensional Lie algebras of Virasoro type and moduli spaces of curves, suggested by string theory. We will see that the infinitesimal geometry of determinant bundles is governed by Virasoro symmetries. The Mumford forms are just invariants of these symmetries. The representations of Virasoro algebra define (twisted)D-modules on moduli spaces; theseD-modules are equations on correlators in conformal field theory.

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