The essential skeleton of a product of degenerations
The essential skeleton of a product of degenerations
We study the problem of how the dual complex of the special fiber of a strict normal crossings degeneration $\mathscr{X}_{R}$ changes under products. We view the dual complex as a skeleton inside the Berkovich space associated to $X_{K}$ . Using the Kato fan, we define a skeleton $\text{Sk}(\mathscr{X}_{R})$ when the …