48 citations · 157 across the 21 of their papers we have counts for
5 papers · 2 filters
Positivity functions for curves on algebraic varieties
Brian Lehmann, Jian Xiao
This is the second part of our work on Zariski decomposition structures, where we compare two different volume type functions for curve classes. The first function is the polar tra…
Correspondences between convex geometry and complex geometry
Brian Lehmann, Jian Xiao
We present several analogies between convex geometry and the theory of holomorphic line bundles on smooth projective varieties or Kähler manifolds. We study the relation between po…
On the geometry of thin exceptional sets in Manin's Conjecture
Brian Lehmann, Sho Tanimoto
Manin's Conjecture predicts the rate of growth of rational points of a bounded height after removing those lying on an exceptional set. We study whether the exceptional set in Mani…
Morphisms and faces of pseudo-effective cones
Mihai Fulger, Brian Lehmann
Let be a morphism of projective varieties and suppose that is a pseudo-effective numerical cycle class satisfying . A conjecture of Debarre, Jiang, and Vo…
Volume-type functions for numerical cycle classes
Brian Lehmann
A numerical equivalence class of k-cycles is said to be big if it lies in the interior of the closed cone generated by effective classes. We construct analogues for arbitrary cycle…