Study of vector bundles using the theory of complexes

本文研究了交换曲面和K3曲面上Bridgeland稳定对象的模，特别证明了模空间是投射簇，并研究了这类空间的双有理性质。我也将这些结果应用到阿贝尔曲面上向量丛的分类。我还证明了维滕猜想的唐纳森不变量的代数曲面。

I studied moduli of Bridgeland stable objects on an abelian or a K3 surface.In particular, I proved that moduli spaces are projective varieties, and studied birational properties of the spaces. I also apply these results to the classification of vector bundles on abelian surfaces. I also proved the Witten conjecture of Donaldson invariants for algebraic surfaces.