Poincare biextension and ideles on the algebraic curve

Arbarello, de Concini, and Kac have constructed a central extension of the ideles group on a smooth projective algebraic curve. We show a relation of this central extension with the theta-bundle and the Poincare biextension of the Jacobian of the curve. As an application we get a new proof of the adelic formula for the Weil pairing.Comment: 10 pages; this is a shortened and a clearer version of the previous text; some references adde