Squares of positive $(p,p)$-forms

TL;DR

The paper proves that the square of a positive (2,2)-form remains positive, but this property does not extend to forms of higher degree, highlighting a specific positivity preservation in complex geometry.

Contribution

It establishes the positivity preservation of squares for positive (2,2)-forms and demonstrates the failure of this property for higher-degree forms.

Findings

Square of positive (2,2)-forms remains positive.

Positivity does not hold for squares of higher-degree forms.

Provides insight into positivity properties in complex differential geometry.

Abstract

We show that if $\alpha$ is a positive $(2,2)$-form then so is $\alpha^2$. We also prove that this is no longer true for forms of higher degree.