Geodesic
Purity of boundaries of open complex varieties
Journal of Singularities, Tome 4 (2012), pp. 171-179

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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.
DOI : 10.5427/jsing.2012.4j
Classification : 32S35, 55N33, 14E15, 32S20 
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     author = {Andrzej Weber},
     title = {Purity of boundaries of open complex varieties},
     journal = {Journal of Singularities},
     pages = {171--179},
     publisher = {mathdoc},
     volume = {4},
     year = {2012},
     doi = {10.5427/jsing.2012.4j},
     url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2012.4j/}
}
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Andrzej Weber. Purity of boundaries of open complex varieties. Journal of Singularities, Tome 4 (2012), pp. 171-179. doi: 10.5427/jsing.2012.4j

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