Ricerc@Sapienza

Let V be a compact and irreducible complex space of complex dimension v whose regular part is endowed with a complete Hermitian metric h. Let π: M→V be a resolution of V. Under suitable assumptions we show that the (v,q) L2 dbar cohomology of the regular part of V is isomorphic to the (v,q) dbar cohomology of M.
Then we show that the previous isomorphism applies to the case of Saper-type Kähler metrics, as introduced by Grant Melles and Milman, and to the case of complete Kähler metrics with finite volume and pinched negative sectional curvatures.

Let (X,h) be a compact and irreducible Hermitian complex space. This paper is devoted to various questions concerning the analytic K-homology of (X,h)⁠. In the 1st part, assuming either dim(sing(X))=0 or dim(X)=2⁠, we show that the rolled-up operator of the minimal L2-Dolbeault- complex, denoted here ð_rel⁠, induces a class in K_0(X)≡KK_0(C(X),C)⁠. A similar result, assuming dim(sing(X))=0⁠, is proved also for ð_abs⁠, the rolled-up operator of the maximal L2-Dolbeault-complex.

Let M be a compact complex manifold. In this paper we give a simple proof of the bimeromorphic invariance of the higher Todd genera of M, a result first proved implicitly by Brasselet, Schurmann e Yokura using algebraic methods.