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.
Information
Published: 1 January 2010
First available in Project Euclid: 24 November 2018
zbMATH: 1214.14033
MathSciNet: MR2761931
Digital Object Identifier: 10.2969/aspm/06010259
Subjects:
Primary:
14J10
,
14J17
,
14J29
,
53D05
Keywords:
$\mathbb{Q}$-Gorenstein smoothing
,
bidouble cover
Rights: Copyright © 2010 Mathematical Society of Japan
