English

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

Algebraic Geometry 2010-03-15 v2 Geometric Topology

Abstract

We show that there is a complex structure on the symplectic 4-manifold W4,kW_{4, k} obtained from the elliptic surface E(4) by rationally blowing down kk sections for 2k92\le k\le 9. And we interpret it via Q{\mathbb Q}-Gorenstein smoothing. This answers affirmatively to a question raised by R. Gompf.

Keywords

Cite

@article{arxiv.0905.3705,
  title  = {Complex structure on the rational blowdown of sections in E(4)},
  author = {Yongnam Lee},
  journal= {arXiv preprint arXiv:0905.3705},
  year   = {2010}
}

Comments

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

R2 v1 2026-06-21T13:05:03.894Z