The essential skeleton of a product of degenerations

  title={The essential skeleton of a product of degenerations},
  author={Morgan V. Brown and Enrica Mazzon},
  journal={Compositio Mathematica},
  pages={1259 - 1300}
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 model $\mathscr{X}_{R}$ is log-regular. We show that if $\mathscr{X}_{R}$ and $\mathscr{Y}_{R}$ are log-smooth, and at least one is semistable, then $\text{Sk}(\mathscr{X}_{R… Expand
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