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Equivariant autoequivalences for finite group actions

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arxiv math/0508625 v1 pith:7ZISOAYW submitted 2005-08-30 math.AG

David Ploog This is my paper · ORCID
classification math.AG
keywords groupautoequivalencesequivariantfinitesurfacesactionsactsapply
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abstract

The familiar Fourier-Mukai technique can be extended to an equivariant setting where a finite group $G$ acts on a smooth projective variety $X$. In this paper we compare the group of invariant autoequivalences $\Aut(D(X))^G$ with the group of autoequivalences of $D^G(X)$. We apply this method in three cases: Hilbert schemes on K3 surfaces, Kummer surfaces and canonical quotients.

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  1. Kuznetsov components ans transcendental motives of cubic fourfolds

    math.AG 2026-05 unverdicted novelty 5.0 of 10

    For Fourier-Mukai partners X and Y among special cubic fourfolds, t(X) ≅ t(Y), with explicit descriptions in rational and conjecturally irrational cases plus an equivariant construction for order-3 automorphisms.

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