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arXiv · 2503.08419

Reconstruction theorems in the supported case

Luigi Lombardi
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Abstract

We show that any equivalence of bounded derived categories of coherent sheaves on a smooth projective complex variety supported in a closed algebraic subset preserves the dimension of the support in two cases: (i) the restriction of the (anti)canonical bundle to the support is ample; (ii) the supports are irreducible and the equivalence sends a skyscraper sheaf of a closed point to a skyscraper sheaf of a closed point. Moreover, in the first case the equivalence recovers the set of closed points of the support up to homeomorphism.

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Luigi Lombardi. 2025-03-11. Reconstruction theorems in the supported case. https://arxiv.org/abs/2503.08419

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