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no. 4
The structure of exceptional sequences on toric varieties of Picard rank two
Altmann, Klaus1; Witt, Frederik2
1 Institut für Mathematik, FU Berlin, Königin-Luise-Str. 24-26, D-14195 Berlin
2 Fachbereich Mathematik, U Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart
Algebraic Combinatorics, Volume 7 (2024) no. 4, pp. 1039-1074.

For a smooth projective toric variety of Picard rank two we classify all exceptional sequences of invertible sheaves which have maximal length. In particular, we prove that unlike non-maximal sequences, they (a) remain exceptional under lexicographical reordering, (b) satisfy strong spatial constraints in the Picard lattice, and (c) are full, that is, they generate the derived category of the variety.

Received:
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Published online:
DOI: 10.5802/alco.371
Classification: 14F08, 14M25, 52C05
Keywords: toric variety, derived category, exceptional sequence

Altmann, Klaus 1; Witt, Frederik 2

1 Institut für Mathematik, FU Berlin, Königin-Luise-Str. 24-26, D-14195 Berlin
2 Fachbereich Mathematik, U Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Altmann, Klaus; Witt, Frederik. The structure of exceptional sequences on toric varieties of Picard rank two. Algebraic Combinatorics, Volume 7 (2024) no. 4, pp. 1039-1074. doi : 10.5802/alco.371. https://alco.centre-mersenne.org/articles/10.5802/alco.371/

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