Rouquier dimension is Krull dimension for normal toric varieties

David Favero; Jesse Huang

Rouquier dimension is Krull dimension for normal toric varieties

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arxiv 2302.09158 v2 pith:PYGUB6HJ submitted 2023-02-17 math.AG

David Favero , Jesse Huang This is my paper · ORCID

classification math.AG

keywords dimensionrouquierkrullnormalsheavestoricboundedcategories

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We prove that for any normal toric variety, the Rouquier dimension of its bounded derived category of coherent sheaves is equal to its Krull dimension. Our proof uses the coherent-constructible correspondence to translate the problem into the study of Rouquier dimension for certain categories of constructible sheaves.

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Line Bundle Resolutions via the Coherent-Constructible Correspondence
math.AG 2024-11 accept novelty 6.0 of 10

On smooth projective toric varieties, every coherent sheaf has a minimal line bundle resolution of length at most the dimension, and for toric subvarieties the Betti numbers are compactly supported cohomology groups o...

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