Algebraically trivial automorphisms of irreducible holomorphic symplectic manifolds

Abstract

We extend the lattice-theoretic approach of Brandhorst--Cattaneo to classify algebraically trivial actions on the known IHS manifolds, up to deformation and birational conjugacy. In particular, we classify even order algebraically trivial nonsymplectic automorphisms, with or without trivial discriminant action. In the case of nontrivial discriminant actions, we show that such automorphisms exist only for finitely many known deformation types and orders.

46 pages, 5 tables. Better focus in introduction; preliminaries reworked; the statements and proofs in Section 4.3 revised; classification results corrected after finding wrong entries in Table 5; tables of results moved in a new appendix; new examples and remarks in Section 5. Comments welcome!