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arXiv · 2407.20896

The degeneration of a family of rational surface automorphisms

Qitong Jiang
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Abstract

We consider a one-dimensional family of rational surfaces with automorphisms. In a degeneration of this family, the limiting map is the identity map on a special fiber. We check that the map on the total space of the family has indeterminacy in the special fiber. However, we show that after blowing-up at an indeterminate curve, there is an induced birational map on the exceptional divisor over the indeterminate curve. Moreover, we show that this map has dynamical degree 16.

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Qitong Jiang. 2024-07-30. The degeneration of a family of rational surface automorphisms. https://doi.org/10.1007/s40879-026-00888-3

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