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Teoreticheskaya i Matematicheskaya Fizika, 2015, Volume 185, Number 2, Pages 313–328
DOI: https://doi.org/10.4213/tmf8934 (Mi tmf8934) 		 
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
Full-text PDF (503 kB) Citations (1)
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DOI: https://doi.org/10.4213/tmf8934
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.
Funding agency Grant number
Russian Science Foundation 14-50-00005
Received: 29.12.2014
English version:
Theoretical and Mathematical Physics, 2015, Volume 185, Issue 2, Pages 1636–1648
DOI: https://doi.org/10.1007/s11232-015-0369-9
Bibliographic databases:
Document Type: Article
Language: Russian
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
Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf8934
  • https://www.mathnet.ru/eng/tmf/v185/i2/p313
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:59
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