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Working paper

Embeddings of groups Aut(F_n) into automorphism groups of algebraic varieties

arxiv.org. math. Cornell University, 2021. No. 2106.02072.
For each integer n>0, we construct a series of irreducible algebraic varieties X, for which the automorphism group Aut(X) contains as a subgroup the automorphism group Aut(F_n) of a free group F_n of rank n. For n > 1, such groups Aut(X) are nonamenable, and for n > 2, they are nonlinear and contain the braid group B_n. Some of these varieties X are affine, and among affine, some are rational and some are not, some are smooth and some are singular. The byproduct is that for n > 2, each Cremona group of rank > 3n-1 contains Aut(F_n) and the braid group B_n.