On the full, strongly exceptional collections on toric varieties with Picard number three

2010/03/10 by Michał Lasoń, Michal Lason, Mateusz Michałek +1 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Algebra over a field #Algebraic Geometry and Number Theory #Bundle #Commutative Algebra and Its Applications #Line bundle #Mathematics #Morphism #Picard group #Pure mathematics #math.AG

paper · pdf · doi:10.1007/s13348-011-0044-x

published as Collectanea Mathematica 62 (2011), no. 3, 275-296

arxiv created 2010/03/10 · openalex publication_date 2011/05/27 · arxiv updated 2021/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We investigate full strongly exceptional collections on smooth, complete toric varieties. We obtain explicit results for a large family of varieties with Picard number three, containing many of the families already known. We also describe the relations between the collections and the split of the push forward of the trivial line bundle by the toric Frobenius morphism.

Citations

• Fourier-Mukai Transforms in Algebraic Geometry
• Derived category of toric varieties with Picard number three
• Introduction to Toric Varieties. (AM-131)

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• Equivalent condition for approximately Cohen–Macaulay complexes