THE CHERN CHARACTER OF A PARABOLIC BUNDLE AND A PARABOLIC REZNIKOV THEOREM IN THE CASE OF FINITE

ar X iv :m at h/ 06 12 14 4v 2 [m ath .A G] 2 Fe b 2 00 7 THE CHERN CHARACTER OF A PARABOLIC BUNDLE, AND A PARABOLIC REZNIKOV THEOREM IN THE CASE OF FINITE ORDER AT INFINITY JAYA NN IYER AND CARLOS T SIMPSON Abstract. In this paper, we obtain an explicit formula for the Chern character of a locally abelian parabolic bundle in terms of its constituent bundles. Several features and variants of parabolic structures are discussed. Parabolic bundles arising from logarithmic connections form an important class of examples. As an application, we consider the situation when the local monodromies are semi-simple and are of finite order at infinity. In this case the parabolic Chern classes of the associated locally abelian parabolic bundle are deduced to be zero in the rational Deligne cohomology in degrees ≥ 2. 1. Introduction Parabolic bundles were introduced by Mehta and Seshadri [Me-Se] [Se] over curves and the definition was extended over higher dimensional varieties by Maruyama and Yokogawa [Ma-Yo] Biswas [Bi], Li [Li], Steer-Wren [Sr-Wr], Panov [Pa] and Mochizuki [Mo2]. A parabolic bundle F on a variety X is a collection of vector bundles F?, indexed by a set of weights, i.

• parabolic reznikov


• maruyama-yokogawa's original


• characteristic classes


• over


• locally abelian


• deligne chern


• bundles based


• parabolic bundles


• bundles involving