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arXiv · 2112.13298

The behavior of essential dimension under specialization II

Zinovy Reichstein·Federico Scavia
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Abstract

Let $G$ be a linear algebraic group over a field. We show that, under mild assumptions, in a family of primitive generically free $G$-varieties over a base variety $B$ the essential dimension of the geometric fibers may drop on a countable union of Zariski closed subsets of $B$ and stays constant away from this countable union. We give several applications of this result.

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Zinovy Reichstein, Federico Scavia. 2021-12-25. The behavior of essential dimension under specialization II. https://doi.org/10.2140/ant.2023.17.1925

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