Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8904652 | Advances in Mathematics | 2018 | 32 Pages |
Abstract
We study how the geometry of a projective variety X is reflected in the positivity properties of the diagonal ÎX considered as a cycle on XÃX. 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 ÎX is big, we prove that the Hodge groups Hk,0(X) vanish for k>0. We also classify varieties of low dimension where the diagonal is nef and big.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Brian Lehmann, John Christian Ottem,