Zhang Weiyi
Abstract: The Kodaira dimension, for complex manifolds was introduced by Kodaira more than 50 years ago, and has played an important role in the classification theory, especially for complex surfaces. In the symplectic world, this notion has been defined only for manifolds with dimension two and four. Some preliminary classification has also been achieved. We can also naturally introduce a Kodaira dimension for a 4-dimensional Lefschetz fibration when the base has genus at least one. We will discuss the equivalence of these different Kodaira dimensions. Finally, we will present a new interpretation of symplectic Kodaira dimension in dimension 4. We use this to generalize our results to some Lefschetz fibration when the base is a sphere.