Complete subvarieties in the projectivized strata of meromorphic differentials

TL;DR

The paper constructs a global plurisubharmonic function on projectivized strata of meromorphic differentials, providing a flat-geometric proof that these strata lack positive-dimensional complete subvarieties.

Contribution

It offers an explicit construction of a globally defined strictly plurisubharmonic function on these strata, establishing a new geometric property.

Findings

Strata of meromorphic differentials do not contain positive-dimensional complete subvarieties.

Provides a flat-geometric proof of this non-existence.

Constructs an explicit globally defined strictly plurisubharmonic function.

Abstract

Here we give an explicit construction of a globally defined strictly plurisubharmonic function on projectivized strata of strictly meromorphic differentials with prescribed orders of zeros and poles. In particular, this yields a flat-geometric proof that these strata do not contain positive-dimensional complete subvarieties.