BETTI NUMBERS OF SHIMURA CURVES AND ARITHMETIC THREE--ORBIFOLDS

The non-cocompact arithmetic lattices in SL 2 ( C ) are all commensurable to one of the Bianchi groups [30, Theorem 8.2.3], and it is not very hard to deduce Theorem 1.1 in the case

We call a K¨ ahler orbifold to be of Hodge type, if the K¨ ahler form is the Chern form of a positive orbifold line bundle.A theorem of Baily [2] states that in this case the

The key to Theorem 1.7 is a celebrated theorem of Gromov, see [6], that bounds the Betti numbers of an analytic manifold with sectional curvatures in [−1, 0] and no local

In the last part of this paper we will also provide a simple description of a 1-category (Ho) whose objects are reduced orbifold structures (i.e. classes of equivalent re-

Our construction combines an appropriate desingularization of any Riemannian orbifold by a fo- liated smooth manifold, with the foliated equivariant quantization that we built

Study of projective equivalence of connections Origins: Goes back to the twenties and thirties Objective: Associate a unique connection to each projective structure [∇]. First

coordinate functions satisfy will give some equations that define the curve and that allow us to compute its points..

In [12], it is given a method to compute equations for Atkin-Lehner quotients of Shimura curves attached to an odd discriminant D which are hyperelliptic over Q and some equations