paper

The behavior of essential dimension under specialization II

arXiv:2112.13298 · doi:10.2140/ant.2023.17.1925

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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