Stability conditions and positivity of invariants of fibrations

Abstract

We study three methods that prove the positivity of a natural numerical invariant associated to $1-$parameter families of polarized varieties. All these methods involve different stability conditions. In dimension 2 we prove that there is a natural connection between them, related to a yet another stability condition, the linear stability. Finally we make some speculations and prove new results in higher dimension.

arXiv commentFinal version, to appear in the Springer volume dedicated to Klaus Hulek on the occasion of his 60-th birthday