Geodesic
The differential geometry of blow-ups
Teoretičeskaâ i matematičeskaâ fizika, Tome 185 (2015) no. 2, pp. 313-328 Cet article a éte moissonné depuis la source Math-Net.Ru

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We discuss the local geometry in the vicinity of a sphere $\mathbb P^1$ embedded with a negative normal bundle. We show that the behavior of the Kähler potential near a sphere embedded with a given normal bundle can be determined using the adjunction formula. As a by-product, we construct (asymptotically locally complex-hyperbolic) Kähler–Einstein metrics on the total spaces of the line bundles $\mathcal O(-m)$, $m\ge3$, over $\mathbb P^1$.
Keywords: blow-up, adjunction formula
Mots-clés : Kähler–Einstein metric. 
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D. V. Bykov. The differential geometry of blow-ups. Teoretičeskaâ i matematičeskaâ fizika, Tome 185 (2015) no. 2, pp. 313-328. http://geodesic.mathdoc.fr/item/TMF_2015_185_2_a4/

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