Derived Categories of Toric Varieties

2005/03/05 by Yūjirō Kawamata, Yujiro Kawamata, Kawamata, Yujiro · 11 citations
Mathematics · #13D99 #14E30 #14F17 #14J17 #14M25 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #math.AG #msc:13D99 #msc:14E30 #msc:14F17 #msc:14J17 #msc:14M25

paper · pdf · doi:10.48550/arxiv.math/0503102

24 pages

openalex publication_date 2005/03/05 · arxiv created 2005/04/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the derived categories for toric varieties have complete exceptional collections.

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• Cellular free resolutions for normalizations of toric ideals
• Geometric Construction of Quiver Tensor Products
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• Exceptional Collections for Toric Fano Fivefolds
• Strata of toric hyperplane arrangements, zonotope lattice points, and the Bondal-Thomsen collection
• Equivariant localizing invariants of simple varieties
• Generating systems, generalized Thomsen collections and derived categories of toric varieties
• Contact isotopies in the coherent-constructible correspondence
• The geometry of Frobenius on toric varieties
• Computing higher direct images in Macaulay2

Related

• Derived categories of toric varieties II
• Derived category of toric fibrations
• Strong full exceptional collections on certain toric varieties with Picard number three via mutations
• Derived categories of toric varieties III
• Selected topics on Toric Varieties