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