Symplectic invariance of rational surfaces on Kähler manifolds

Jason Michael Starr

Published 2018-03-16Version 1

By work of Koll\'{a}r and Ruan, uniruledness of K\"{a}hler manifolds is an invariant of the underlying symplectic manifold. Zhiyu Tian proved that rational connectedness is a symplectic invariant if the dimension is $\leq 3$. We prove existence of a covering family of rational surfaces assuming positivity of certain gravitational descendants.