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dc.contributor.authorDunajski, Maciejen
dc.contributor.authorTod, Paulen
dc.date.accessioned2020-02-06T10:50:38Z
dc.date.available2020-02-06T10:50:38Z
dc.identifier.issn1093-6106
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/301776
dc.description.abstractWe describe the range of the Radon transform on the space $M$ of irreducible conics in $\CP^2$ in terms of natural differential operators associated to the $SO(3)$-structure on $M=SL(3, \R)/SO(3)$ and its complexification. Following \cite{moraru} we show that for any function $F$ in this range, the zero locus of $F$ is a four-manifold admitting an anti-self-dual conformal structure which contains three different scalar-flat K\"ahler metrics. The corresponding twistor space ${\mathcal Z}$ admits a holomorphic fibration over $\CP^2$. In the special case where ${\mathcal Z}=\CP^3\setminus\CP^1$ the twistor lines project down to a four-parameter family of conics which form triangular Poncelet pairs with a fixed base conic.
dc.description.sponsorshipThe work of M.D. has been partially supported by STFC consolidated grant no. ST/P000681/1. Part of this work was done while P.T. held the Brenda Ryman Visiting Fellowship in the Sciences at Girton College, Cambridge, and he gratefully acknowledges the hospitality of the College.
dc.publisherInternational Press of Boston, Inc.
dc.rightsAll rights reserved
dc.titleConics, Twistors, and anti-self-dual tri-Kähler metricsen
dc.typeArticle
prism.publicationNameAsian Journal of Mathematicsen
dc.identifier.doi10.17863/CAM.22292
dcterms.dateAccepted2019-12-09en
rioxxterms.versionAM
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserveden
rioxxterms.licenseref.startdate2019-12-09en
dc.identifier.eissn1945-0036
rioxxterms.typeJournal Article/Reviewen
cam.orpheus.counter90*
rioxxterms.freetoread.startdate2023-02-06


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