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    Smooth Complete Intersections with Positive-Definite Intersection Form

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    Smirnov_Ilia_201210_MSC.pdf (576.0Kb)
    Date
    2012-10-16
    Author
    Smirnov, Ilia
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    Abstract
    We classify the smooth complete intersections with positive-definite intersection form on their middle cohomology. There are two families. The first family are quadric hypersurfaces in P(4k+1) with k a positive integer. The middle cohomology is always of rank two and the intersection lattice corresponds to the identity matrix. The second family are complete intersections of two quadrics in P(4k+2) (k a positive integer). Here the intersection lattices are the Gamma(4(k+1)) lattices; in particular, the intersection lattice of a smooth complete intersection of two quadrics in P(6) is the famous E8 lattice.
    URI for this record
    http://hdl.handle.net/1974/7602
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