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Does anybody know a reference in which the computation of the cohomology of a blow-up is made in detail?

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Have you looked into SGA5, section VII? –  Konrad Voelkel Jun 30 '13 at 9:48
    
Thanks Konrad. Is this available online? –  memon Jun 30 '13 at 9:57
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googling immediately gives you this: library.msri.org/books/sga/sga5/index.html –  Konrad Voelkel Jun 30 '13 at 10:05
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or SGA7, vol. II, p.258. –  shenghao Jun 30 '13 at 10:46
    
Another alternative: Griffiths and Harris, Chapter 4, Section 6, subsection "Blowing Up Submanifolds." –  Charles Staats Jun 30 '13 at 18:45
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