A special Lagrangian type equation for holomorphic line bundles

作者：Jacob Adam^*; Yau Shing Tung

来源：Mathematische Annalen, 2017, 369(1-2): 869-898.

DOI：10.1007/s00208-016-1467-1

Let L be a holomorphic line bundle over a compact Kahler manifold X. Motivated by mirror symmetry, we study the deformed Hermitian-Yang-Mills equation on L, which is the line bundle analogue of the special Lagrangian equation in the case that X is Calabi-Yau. We show that this equation is the Euler-Lagrange equation for a positive functional, and that solutions are unique global minimizers. We provide a necessary and sufficient criterion for existence in the case that X is a Kahler surface. For the higher dimensional cases, we introduce a line bundle version of the Lagrangian mean curvature flow, and prove convergence when L is ample and X has non-negative orthogonal bisectional curvature.

• 出版日期2017-10