Generic positivity and applications to hyperbolicity of moduli spaces
arXiv:1610.09832
Abstract
The proof of the celebrated Viehweg's hyperbolicity conjecture is a consequence of two remarkable results: Viehweg and Zuo's existence results for global pluri-differential forms induced by variation in a family of canonically po-larised manifolds and Campana and Pǎun's vast generalisation of Miyaoka's generic semipositivity result for non-uniruled varieties to the context of pairs. The aim of this chapter is an exposition of Campana-Pǎun's generic semipositivity theorem .
arXiv comment30 pages. To appear as a chapter of a book about complex hyperbolicity
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- Equality in the Miyaoka-Yau inequality and uniformization of non-positively curved klt pairs
- Almost nef regular foliations and Fujita's decomposition of reflexive sheaves
- Structure of projective varieties with nef anticanonical divisor: the case of log terminal singularities
- Towards classification of codimension 1 foliations on threefolds of general type