Orthogonally spherical objects and spherical fibrations

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:	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:	07 Nov 2023 01:50
URI:	https://orca.cardiff.ac.uk/id/eprint/81428

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