Direct images of pseudoeffective cotangent bundles
- Resource Type
- Working Paper
- Authors
- Cao, Junyan; Höring, Andreas
- Source
- Subject
- Mathematics - Algebraic Geometry
Mathematics - Complex Variables
14J60, 14D06, 14E30, 37F75
- Language
Let A be an elliptic curve, and let $V_A$ be the Serre vector bundle on A. A famous example of Demailly-Peternell-Schneider shows that the tautological class of $V_A$ contains a unique closed positive current. In this survey we start by generalising this statement to arbitrary compact K\"ahler manifolds. We then give an application to abelian fibrations $X \rightarrow Y$ where the total space X has pseudoeffective cotangent bundle and raise some questions about nonvanishing properties of these bundles.
Comment: 31 pages