Positivity of the diagonal

2017/07/26 by Lehmann, Brian, Ottem, John Christian · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1707.08659

Abstract

We study how the geometry of a projective variety X is reflected in the positivity properties of the diagonal Δ_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 diagonal is big, we prove that the Hodge groups H^k,0(X) vanish for k>0. We also classify varieties of low dimension where the diagonal is nef and big.

Cited by

• When is the diagonal contractible?

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