10.46298/epiga.2017.volume1.2038
Lehmann, Brian
Brian
Lehmann
Xiao, Jian
Jian
Xiao
Correspondences between convex geometry and complex geometry
episciences.org
2017
Mathematics - Algebraic Geometry
Mathematics - Complex Variables
contact@episciences.org
episciences.org
2017-07-10T09:09:59+02:00
2021-02-08T12:04:30+01:00
2017-09-01
eng
Journal article
https://epiga.episciences.org/2038
arXiv:1607.06161
2491-6765
PDF
1
Épijournal de Géométrie Algébrique ; Volume 1 ; 2491-6765
We present several analogies between convex geometry and the theory of
holomorphic line bundles on smooth projective varieties or K\"ahler 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.
Comment: EpiGA Volume 1 (2017), Article Nr. 6