Volume of strata of abelian differentials

Question

I am reading this paper https://arxiv.org/pdf/math/0006171.pdf on the volume of strata in the moduli space of abelian differentials, and just have a small clarificatory question.

On page 4, the volume of a subset $ E \subset\mathcal{H}_1(\mu)$ is defined to be $vol(C\Phi(E))$, where the volume is with respect to the Lebesgue measure over the "cone over $\Phi(E)$ with vertex at origin".

What does this cone refer to? Does it mean all scalar multiples of points in $\Phi(E)$ with the scalar between 0 and 1 or something?

Thanks!

Answer 1

I found the answer here: https://arxiv.org/abs/1612.08374.

The cone $C_RF \subset \mathcal{H}(\mu)$ 'over' a set $F$ is defined as $$C_RF:=\{(X,r\cdot \omega)\vert(X,\omega)\in F,0<r\le R \}$$