Lehmann, Brian and Xiao, Jian - Correspondences between convex geometry and complex geometry

epiga:2038 - Épijournal de Géométrie Algébrique, September 1, 2017, Volume 1
Correspondences between convex geometry and complex geometry

Authors: Lehmann, Brian and Xiao, Jian

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 positive products and mixed volumes. We define and study a Blaschke addition for divisor classes and mixed divisor classes, and prove new geometric inequalities for divisor classes. We also reinterpret several classical convex geometry results in the context of algebraic geometry: the Alexandrov body construction is the convex geometry version of divisorial Zariski decomposition; Minkowski's existence theorem is the convex geometry version of the duality between the pseudo-effective cone of divisors and the movable cone of curves.


Volume: Volume 1
Published on: September 1, 2017
Submitted on: July 10, 2017
Keywords: Mathematics - Algebraic Geometry,Mathematics - Complex Variables


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