Coverings with prescribed ramification and Virasoro groups

Geometric approach to Kac–Moody and Virasoro algebras

“…Our approach can be viewed as a generalization of previous works [7,25]. In fact, if we restrict ourselves to the rank 1 case and look at the level of tangent spaces, then the relation to the results of Arbarello et al [7] becomes apparent.…”

“…In other words, we can explicitly identify T E U ∞ g (n, d) with a subspace of T E Gr χ (V ). Let M ∞ g denote the moduli space of triples (X, x, z), where X has genus g. We know that [17,25] T W Gr(V )…”

“…In fact, if we restrict ourselves to the rank 1 case and look at the level of tangent spaces, then the relation to the results of Arbarello et al [7] becomes apparent. Furthermore, here we are essentially studying bundles on curves, whereas Muñoz Porras and Plaza Martín [25] deal with coverings of curves; the techniques and goals are, however, similar and closely related. = sl C((z)) (V ) g (where sl C((z)) (V ) denotes the Lie algebra of the special linear group) and the second rational cohomology group of the moduli space parametrizing four-tuples consisting of a curve, a point, a tangent vector and a rank-2 vector bundle with fixed determinant [28].…”