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Creators/Authors contains: "Lyubeznik, Gennady"

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  1. ; ; ; ; (, International Mathematics Research Notices)
    Full Text Available 
  2. ; ; ; ; (, Mathematische Annalen)
    null (Ed.)
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  3. ; ; ; ; (, Mathematische Annalen)
    null (Ed.)
    Accepted Manuscript Full Text Available
  4. ; (, Proceedings of the American Mathematical Society)
    Accepted Manuscript Full Text Available
  5. ; (, Proceedings of the American Mathematical Society)
    Accepted Manuscript Full Text Available
  6. ; ; ; ; (, American journal of mathematics)
    For a local complete intersection subvariety $X = V (I)$ in $P^n$ over a field of characteristic zero, we show that, in cohomological degrees smaller than the codimension of the singular locus of $$X$$, the cohomology of vector bundles on the formal completion of $P^n$ along $$X$$ can be effectively computed as the cohomology on any sufficiently high thickening $$X_t = V (I^t)$$; the main ingredient here is a positivity result for the normal bundle of $$X$$. Furthermore, we show that the Kodaira vanishing theorem holds for all thickenings $$X_t$$ in the same range of cohomological degrees; this extends the known version of Kodaira vanishing on $$X$$, and the main new ingredient is a version of the Kodaira- Akizuki-Nakano vanishing theorem for $$X$$, formulated in terms of the cotangent complex. 
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  7. ; ; ; ; (, American Journal of Mathematics)
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