Exceptional collections of line bundles on the Beauville surface

Sergey Galkin; Evgeny Shinder

doi:10.1016/j.aim.2013.06.007

Exceptional collections of line bundles on the Beauville surface

Sergey Galkin, Evgeny Shinder

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract / Description of output

We construct quasi-phantom admissible subcategories in the derived category of coherent sheaves on the Beauville surface S. These quasi-phantoms subcategories appear as right orthogonals to subcategories generated by exceptional collections of maximal possible length 4 on S. We prove that there are exactly 6 exceptional collections consisting of line bundles (up to a twist) and these collections are spires of two helices.

Original language	English
Pages (from-to)	1033-1050
Journal	Advances in Mathematics
Volume	244
DOIs	https://doi.org/10.1016/j.aim.2013.06.007
Publication status	Published - 10 Sept 2013

Keywords / Materials (for Non-textual outputs)

math.AG
math.KT

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10.1016/j.aim.2013.06.007

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title = "Exceptional collections of line bundles on the Beauville surface",

abstract = "We construct quasi-phantom admissible subcategories in the derived category of coherent sheaves on the Beauville surface S. These quasi-phantoms subcategories appear as right orthogonals to subcategories generated by exceptional collections of maximal possible length 4 on S. We prove that there are exactly 6 exceptional collections consisting of line bundles (up to a twist) and these collections are spires of two helices.",

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AU - Shinder, Evgeny

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N2 - We construct quasi-phantom admissible subcategories in the derived category of coherent sheaves on the Beauville surface S. These quasi-phantoms subcategories appear as right orthogonals to subcategories generated by exceptional collections of maximal possible length 4 on S. We prove that there are exactly 6 exceptional collections consisting of line bundles (up to a twist) and these collections are spires of two helices.

AB - We construct quasi-phantom admissible subcategories in the derived category of coherent sheaves on the Beauville surface S. These quasi-phantoms subcategories appear as right orthogonals to subcategories generated by exceptional collections of maximal possible length 4 on S. We prove that there are exactly 6 exceptional collections consisting of line bundles (up to a twist) and these collections are spires of two helices.

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KW - math.KT

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DO - 10.1016/j.aim.2013.06.007

M3 - Article

SN - 0001-8708

VL - 244

SP - 1033

EP - 1050

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Exceptional collections of line bundles on the Beauville surface

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