Advanced Studies in Pure Mathematics

Complex structure on the rational blowdown of sections in $E(4)$

Yongnam Lee

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Abstract

We show that there is a complex structure on the symplectic 4-manifold $W_{4,k}$ obtained from the elliptic surface E(4) by rationally blowing down $k$ sections for $2 \leq k \leq 9$. And we interpret it via $\mathbb{Q}$-Gorenstein smoothing. This answers affirmatively to a question raised by R. Gompf.

Article information

Source
Algebraic Geometry in East Asia — Seoul 2008, J. H. Keum, S. Kondō, K. Konno and K. Oguiso, eds. (Tokyo: Mathematical Society of Japan, 2010), 259-269

Dates
Received: 28 May 2009
Revised: 10 March 2010
First available in Project Euclid: 24 November 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1543085644

Digital Object Identifier
doi:10.2969/aspm/06010259

Mathematical Reviews number (MathSciNet)
MR2761931

Zentralblatt MATH identifier
1214.14033

Subjects
Primary: 14J29: Surfaces of general type 14J10: Families, moduli, classification: algebraic theory 14J17: Singularities [See also 14B05, 14E15] 53D05: Symplectic manifolds, general

Keywords
Bidouble cover $\mathbb{Q}$-Gorenstein smoothing

Citation

Lee, Yongnam. Complex structure on the rational blowdown of sections in $E(4)$. Algebraic Geometry in East Asia — Seoul 2008, 259--269, Mathematical Society of Japan, Tokyo, Japan, 2010. doi:10.2969/aspm/06010259. https://projecteuclid.org/euclid.aspm/1543085644


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