课程名称：Donaldson Question: “Tamed to Compatible"
课程简介：In these talks,
we show that on any tamed closed almost complex four-manifold (M,J) whose
dimension of J-anti-invariant cohomology is equal to self-dual second Betti
number minus one, there exists a new symplectic form compatible with the given
almost complex structure J. In particular, if the self-dual second Betti number
is one, we give an affirmative answer to Donaldson question for tamed closed
almost complex four-manifolds that is a conjecture in joint paper of Tosatti,
Weinkove and Yau.
Our approach is
along the lines used by Buchdahl to give a unified proof of the Kodaira
conjecture. Thus, our main result gives an affirmative answer to the Kodaira
conjecture in symplectic version.