Positivity of the Diagonal

نویسندگان

  • BRIAN LEHMANN
  • JOHN CHRISTIAN OTTEM
چکیده

We study how the geometry of a projective variety X is reflected in the positivity properties of the diagonal ∆X considered as a cycle on X ×X. We analyze when the diagonal is big, when it is nef, and when it is rigid. In each case, we give several implications for the geometric properties of X. For example, when the cohomology class of ∆X is big, we prove that the Hodge groups H(X) vanish for k > 0. We also classify varieties of low dimension where the diagonal is nef and big.

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تاریخ انتشار 2017