English

Symplectic invariance of rational surfaces on K\"{a}hler manifolds

Algebraic Geometry 2019-01-31 v3

Abstract

Kollar and Ruan proved symplectic deformation invariance for uniruledness of Kaehler manifolds. Zhiyu Tian proved the same for rational connectedness in dimension < 4. Kollar conjectured this in all dimensions. We prove Kollar's conjecture, as well as existence of a covering family of rational surfaces, for all Kaehler manifolds that are symplectically deformation equivalent to G/P or to a low degree complete intersection in such.

Keywords

Cite

@article{arxiv.1803.06412,
  title  = {Symplectic invariance of rational surfaces on K\"{a}hler manifolds},
  author = {Jason Michael Starr},
  journal= {arXiv preprint arXiv:1803.06412},
  year   = {2019}
}

Comments

37 pages. Revised draft: added statements about Koll{\'a}r's conjecture. Incorporated many suggestions of readers