Closed symmetric differentials which are products of meromorphic differentials

Bruno de Oliveira, February 11th, 2014

The connection between symmetric differentials of degree greater than 1 and the
topology of manifolds is both tenuous and mysterious. Closed symmetric differentials
form a subclass with clearer topological implications. We start with a result showing
that the local decomposition of a closed symmetric differential as a product of closed
1-differentials is essentially of algebraic nature despite being possibly transcendental.
The main result will be about the geometry of holomorphic products of closed
meromorphic 1-differentials.