Anno, Rina and Logvinenko, Timothy  ORCID: https://orcid.org/0000-0001-5279-6977
2016.
Orthogonally spherical objects and spherical fibrations.
Advances in Mathematics
286
, pp. 338-386.
10.1016/j.aim.2015.08.027
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Abstract
We introduce a relative version of the spherical objects of Seidel and Thomas [ST01]. Define an object E in the derived category D(Z×X) to be spherical over Z if the corresponding functor from D(Z) to D(X) gives rise to autoequivalences of D(Z) and D(X) in a certain natural way. Most known examples come from subschemes of X fibred over Z. This categorifies to the notion of an object of D(Z×X) orthogonal over Z. We prove that such an object is spherical over Z if and only if it possesses certain cohomological properties similar to those in the original definition of a spherical object. We then interpret this geometrically in the case when our objects are actual flat fibrations in X over Z.
| Item Type: | Article |
|---|---|
| Date Type: | Publication |
| Status: | Published |
| Schools: | Schools > Mathematics |
| Subjects: | Q Science > QA Mathematics |
| Additional Information: | Under an Elsevier user license |
| Publisher: | Elsevier |
| ISSN: | 0001-8708 |
| Date of First Compliant Deposit: | 30 March 2016 |
| Date of Acceptance: | 25 August 2015 |
| Last Modified: | 29 Nov 2024 08:30 |
| URI: | https://orca.cardiff.ac.uk/id/eprint/81428 |
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