Cohomology of the moduli space of Hecke cycles

Abstract: Let X be a smooth projective curve of genus and let be the moduli space of semistable bundles over X of rank 2 with trivial determinant. Three different desingularizations of have been constructed by Seshadri (Proceedings of the International Symposium on Algebraic Geometry, 1978, 155), Narasimhan–Ramanan (C. P. Ramanujam—A Tribute, 1978, 231), and Kirwan (Proc. London Math. Soc. 65(3) (1992) 474). In this paper, we construct a birational morphism from Kirwan''s desingularization to Narasimhan–Ramanan''s, and prove that the Narasimhan–Ramanan''s desingularization (called the moduli space of Hecke cycles) is the intermediate variety between Kirwan''s and Seshadri''s as was conjectured recently in (Math. Ann. 330 (2004) 491). As a by-product, we compute the cohomology of the moduli space of Hecke cycles. [Copyright &y& Elsevier]