Journal of Singularities
volume 4 (2012), 171-179
Received: 6 June 2012. Received in revised form: 25 October 2012.
We study the boundary of an open smooth complex algebraic variety U. We ask when the cohomology of the geometric boundary Z=X\U in a smooth compactification X is pure with respect to the mixed Hodge structure. Knowing the dimension of singularity locus of some singular compactification, we give a bound for k above which the cohomology H^k(Z) is pure. The main ingredient of the proof is purity of the intersection cohomology sheaf.
Mathematical Subject Classification:
32S35, 55N33, 14E15, 32S20
Department of Mathematics of Warsaw University
Banacha 2, 02-097