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This article is cited in 1 scientific paper (total in 1 paper)
The differential geometry of blow-ups
D. V. Bykov Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
Abstract:
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, Kähler–Einstein metric.
Received: 29.12.2014
Citation:
D. V. Bykov, “The differential geometry of blow-ups”, TMF, 185:2 (2015), 313–328; Theoret. and Math. Phys., 185:2 (2015), 1636–1648
Linking options:
https://www.mathnet.ru/eng/tmf8934https://doi.org/10.4213/tmf8934 https://www.mathnet.ru/eng/tmf/v185/i2/p313
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Abstract page: | 410 | Full-text PDF : | 175 | References: | 59 | First page: | 15 |
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