Sutherland, Tom (2014) Stability conditions for SeibergWitten quivers. PhD thesis, University of Sheffield.

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Abstract
This thesis describes a connected component of the space of numerical stability conditions of certain CY3 triangulated categories using the period map of a meromorphic differential on a family of elliptic curves. The motivation for this result comes from studying meromorphic quadratic differentials on Riemann surfaces. On the one hand, a meromorphic quadratic differential on a Riemann surface defines a double cover, its spectral curve, together with a meromorphic abelian differential on it known as the SeibergWitten differential. On the other hand certain strata of meromorphic quadratic differentials determine a CY3 triangulated category such that the periods of the SeibergWitten differential define the central charge of a stability condition on the category. The simplest examples of this construction involve twodimensional strata of meromorphic quadratic differentials on the Riemann sphere in which case the spectral curves are elliptic curves. There are 10 such strata in bijective correspondence with the Painlev\'{e} equations whose families of spectral elliptic curves include the original examples of SeibergWitten curves and certain degenerations thereof. In these cases the periods of the SeibergWitten differential satisfy a hypergeometric differential equation, so that its period map is described by the Schwarz triangle theorem. In all but one of these examples this period map can be lifted to a map to a canonical connected component of the space of numerical stability conditions of the associated category.
Item Type:  Thesis (PhD) 

Keywords:  Stability conditions, triangulated categories, CalabiYau, SeibergWitten, quivers, quadratic differentials, elliptic curves, periods, hypergeometric 
Academic Units:  The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) 
Identification Number/EthosID:  uk.bl.ethos.605444 
Depositing User:  Mr Tom Sutherland 
Date Deposited:  08 May 2014 09:23 
Last Modified:  03 Oct 2016 11:16 
URI:  http://etheses.whiterose.ac.uk/id/eprint/5808 