dc.contributor.author Dunajski, Maciej en dc.contributor.author Tod, Paul en dc.date.accessioned 2020-02-06T10:50:38Z dc.date.available 2020-02-06T10:50:38Z dc.identifier.issn 1093-6106 dc.identifier.uri https://www.repository.cam.ac.uk/handle/1810/301776 dc.description.abstract We 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.sponsorship The 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.publisher International Press of Boston, Inc. dc.rights All rights reserved dc.title Conics, Twistors, and anti-self-dual tri-Kähler metrics en dc.type Article prism.publicationName Asian Journal of Mathematics en dc.identifier.doi 10.17863/CAM.22292 dcterms.dateAccepted 2019-12-09 en rioxxterms.version AM rioxxterms.licenseref.uri http://www.rioxx.net/licenses/all-rights-reserved en rioxxterms.licenseref.startdate 2019-12-09 en dc.identifier.eissn 1945-0036 rioxxterms.type Journal Article/Review en cam.orpheus.counter 90 * rioxxterms.freetoread.startdate 2023-02-06
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