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The behavior of essential dimension under specialization, II

Zinovy Reichstein and Federico Scavia

Vol. 17 (2023), No. 11, 1925–1958

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.

Received: 5 January 2022
Revised: 15 September 2022
Accepted: 28 November 2022
Published: 3 October 2023
Zinovy Reichstein
Department of Mathematics
University of British Columbia
Vancouver, BC
Federico Scavia
Department of Mathematics
University of California
Los Angeles, CA
United States

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