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Award ID contains: 1800355

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  1. ; ; ; ; (, 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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    Accepted Manuscript Full Text Available
  2. (, Mathematische Zeitschrift)
    Let $$R = k[x_1,...,x_n]$$ be a ring of polynomials over a field $$k$$ of characteristic $p > 0$. There is an algorithm due to Lyubeznik for deciding the vanishing of local cohomology modules $$H_I^i (R)$$ where $$I$$ is an ideal of $$R$$. This algorithm has not been implemented because its complexity grows very rapidly with the growth of p which makes it impractical. In this paper we produce a modification of this algorithm that consumes a modest amount of memory. 
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    Accepted Manuscript Full Text Available
  3. ; (, Proceedings of the American Mathematical Society)
    Accepted Manuscript Full Text Available
  4. ; (, Proceedings of the American Mathematical Society)
    Accepted Manuscript Full Text Available