## Abstract / Description of output

We study sets of commuting reflection functors in the derived category of

sheaves on Calabi-Yau varieties. We show that such a collection is determined by a set of mutually orthogonal spherical objects. We also show that when the spherical objects are locally-free sheaves then the kernel of the composite transform parametrizes properly torsion-free sheaves with zero-dimensional singularity sets and conversely that such a kernel gives rise to a collection of mutually orthogonal spherical vector bundles. We do this using a more detailed analysis of the reason why spherical twists give equivalences.

sheaves on Calabi-Yau varieties. We show that such a collection is determined by a set of mutually orthogonal spherical objects. We also show that when the spherical objects are locally-free sheaves then the kernel of the composite transform parametrizes properly torsion-free sheaves with zero-dimensional singularity sets and conversely that such a kernel gives rise to a collection of mutually orthogonal spherical vector bundles. We do this using a more detailed analysis of the reason why spherical twists give equivalences.

Original language | English |
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Publisher | ArXiv |

Publication status | Published - 2012 |