Geodesic
On the topology of a resolution of isolated singularities, II
Journal of Singularities, Tome 20 (2020), pp. 95-102

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Let Y be a complex projective variety of dimension n with isolated singularities, π: X -> Y a resolution of singularities, G:=π^{-1}(Sing(Y)) the exceptional locus. From the Decomposition Theorem one knows that the map H^{k-1}(G) -> H^k(Y, Y\Sing(Y)) vanishes for k>n. It is also known that, conversely, assuming this vanishing one can prove the Decomposition Theorem for π in few pages. The purpose of the present paper is to exhibit a direct proof of the vanishing. As a consequence, it follows a complete and short proof of the Decomposition Theorem for π, involving only ordinary cohomology.
DOI : 10.5427/jsing.2020.20e
Classification : 14B05, 14C30, 14E15, 14F05, 14F43, 14F45, 32S20, 32S35, 32S60, 58A14, 58K15 
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     author = {Vincenzo Di Gennaro and Davide Franco},
     title = {On the topology of a resolution of isolated singularities, {II}},
     journal = {Journal of Singularities},
     pages = {95--102},
     publisher = {mathdoc},
     volume = {20},
     year = {2020},
     doi = {10.5427/jsing.2020.20e},
     url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2020.20e/}
}
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Vincenzo Di Gennaro; Davide Franco. On the topology of a resolution of isolated singularities, II. Journal of Singularities, Tome 20 (2020), pp. 95-102. doi: 10.5427/jsing.2020.20e

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