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Classification of full exceptional collections on smooth toric Fano varieties with Picard rank two

Classification of full exceptional collections on smooth toric Fano varieties with Picard rank two AbstractIn this paper, we give a complete classification of full exceptional collections, up to cyclic permutations, normalizations and mutations, on smooth toric Fano threefolds and fourfolds with Picard rank two. For such varieties, we find all the exceptional collections of maximal length and show that they are in fact full. This gives a partial answer to a conjecture in [29] and [32]. Moreover, such full exceptional collections essentially arise from Orlov’s theorem on projective bundles. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Geometry de Gruyter

Classification of full exceptional collections on smooth toric Fano varieties with Picard rank two

Lee, Dae-Won
Advances in Geometry , Volume 23 (1): 25 – Jan 1, 2023
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25 pages

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Publisher
de Gruyter
Copyright
© 2023 Walter de Gruyter GmbH, Berlin/Boston
eISSN
1615-715X
DOI
10.1515/advgeom-2022-0025
Publisher site
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Abstract

AbstractIn this paper, we give a complete classification of full exceptional collections, up to cyclic permutations, normalizations and mutations, on smooth toric Fano threefolds and fourfolds with Picard rank two. For such varieties, we find all the exceptional collections of maximal length and show that they are in fact full. This gives a partial answer to a conjecture in [29] and [32]. Moreover, such full exceptional collections essentially arise from Orlov’s theorem on projective bundles.

Journal

Advances in Geometry – de Gruyter

Published: Jan 1, 2023

Keywords: Derived category of coherent sheaves; semiorthogonal decomposition; full exceptional collection; Primary 14J26; Secondary 14M05

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