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

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

2009-05-22

arxiv.org/abs/0905.3705v2

Mathematics

Algebraic Geometry

Minor changes are made. It will apper in Advanced Studies in Pure Mathematics (Proceeding of Algebraic Geometry in East Asia)

Scientific paper

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 $2\le k\le 9$. And we interpret it via ${\mathbb Q}$-Gorenstein
smoothing. This answers affirmatively to a question raised by R. Gompf.

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