Polar Transform and Local Positivity for Curves

TL;DR

This paper introduces new local positivity invariants for curves derived from the polar transform of divisors, providing insights into the structure of non-Kahler loci and extending positivity concepts.

Contribution

It applies convex duality to define novel invariants for curves, bridging divisor positivity and curve positivity in complex geometry.

Findings

New invariants for curves with properties similar to divisor invariants

Characterization of divisorial components of non-Kahler loci

Extension of positivity concepts via polar transform

Abstract

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 positivity invariants for curves. These new invariants have nice properties similar to those for divisors. In particular, this enables us to give a characterization of the divisorial components of the non-Kahler locus of a big class.