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This yields infinitely many 1-parameter families of metrics exhibiting several different behaviours including asymptotically hyperbolic metrics (more specifically of Poincar\u00e9 type), ALF metrics, and metrics which compactify to a Hirzebruch surface <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\mathbb {H}_m$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>H<\/mml:mi>\n                    <mml:mi>m<\/mml:mi>\n                  <\/mml:msub>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> with a cone singularity along the \u201cdivisor at infinity\u201d. This allows us to investigate transitions between behaviours yielding interesting results. For instance, we show that a Ricci\u2013flat ALF metric known as the Taub-bolt metric can be obtained as the limit of a family of cone angle Einstein metrics on <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$${\\mathbb{C}\\mathbb{P}}^2 \\# \\overline{{\\mathbb{C}\\mathbb{P}}}^2$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:msup>\n                      <mml:mrow>\n                        <mml:mi>C<\/mml:mi>\n                        <mml:mi>P<\/mml:mi>\n                      <\/mml:mrow>\n                      <mml:mn>2<\/mml:mn>\n                    <\/mml:msup>\n                    <mml:mo>#<\/mml:mo>\n                    <mml:msup>\n                      <mml:mover>\n                        <mml:mrow>\n                          <mml:mi>C<\/mml:mi>\n                          <mml:mi>P<\/mml:mi>\n                        <\/mml:mrow>\n                        <mml:mo>\u00af<\/mml:mo>\n                      <\/mml:mover>\n                      <mml:mn>2<\/mml:mn>\n                    <\/mml:msup>\n                  <\/mml:mrow>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> when the cone angle converges to zero. We also construct Einstein metrics which are asymptotically hyperbolic and conformal to a scalar-flat K\u00e4hler metric. Such metrics cannot be obtained by applying Derdzi\u0144ski\u2019s theorem.\n<\/jats:p>","DOI":"10.1007\/s12220-025-01975-9","type":"journal-article","created":{"date-parts":[[2025,4,4]],"date-time":"2025-04-04T13:41:40Z","timestamp":1743774100000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Einstein Metrics via Derdzi\u0144ski Duality"],"prefix":"10.1007","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4990-1788","authenticated-orcid":false,"given":"Gon\u00e7alo","family":"Oliveira","sequence":"first","affiliation":[]},{"given":"Rosa","family":"Sena-Dias","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,4,2]]},"reference":[{"issue":"6","key":"1975_CR1","doi-asserted-by":"publisher","first-page":"641","DOI":"10.1142\/S0129167X98000282","volume":"9","author":"M Abreu","year":"1998","unstructured":"Abreu, M.: K\u00e4hler geometry of toric varieties and extremal metrics. 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