15 citations · 38 across the 6 of their papers we have counts for
4 papers · 1 filter
Polar Transform and Local Positivity for Curves
Nicholas McCleerey, Jian Xiao
Using the duality of positive cones, we show that applying the polar transform from convex analysis to local positivity invariants for divisors gives interesting and new local posi…
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…
Convexity and Zariski decomposition structure
Brian Lehmann, Jian Xiao
This is the first part of our work on Zariski decomposition structures, where we study Zariski decompositions using Legendre-Fenchel type transforms. In this way we define a Zarisk…