Purity of boundaries of open complex varieties

Andrzej Weber

Journal of Singularities
volume 4 (2012), 171-179

Received: 6 June 2012. Received in revised form: 25 October 2012.

DOI: 10.5427/jsing.2012.4j

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Abstract:

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.

Keywords:

Mixed Hodge theory of singular varieties, intersection cohomology, resolution of singularities

Mathematical Subject Classification:

32S35, 55N33, 14E15, 32S20

Author(s) information:

Andrzej Weber
Department of Mathematics of Warsaw University
Banacha 2, 02-097
Warszawa, Poland
email: aweber@mimuw.edu.pl