## Advanced Studies in Pure Mathematics

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

Yongnam Lee

#### 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

Dates
Revised: 10 March 2010
First available in Project Euclid: 24 November 2018

https://projecteuclid.org/ euclid.aspm/1543085644

Digital Object Identifier
doi:10.2969/aspm/06010259

Mathematical Reviews number (MathSciNet)
MR2761931

Zentralblatt MATH identifier
1214.14033

#### 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