论文标题
稳定性和变形的Hermitian-yang-mills方程
Stability and the deformed Hermitian-Yang-Mills equation
论文作者
论文摘要
我们调查了变形的Hermitian-yang-mills（DHYM）方程的最新进展。我们讨论了在第一作者和S.-T的工作之后，讨论几何不变理论（GIT）在接近DHYM方程的溶解性中的作用。 Yau。我们将GIT图片与涉及Bridgeland稳定性的Dhym的猜想图片进行了比较。特别是，在Arcara miles之后，我们表明，在$ \ mathbb {p}^2 $ blow上，任何线捆绑包都承认变形的Hermitian-yang-mills方程的解决方案是bridgeland稳定的，但不是在交谈。最后，我们调查了与DHYM方程相关的热流的最新进展。
We survey some recent progress on the deformed Hermitian-Yang-Mills (dHYM) equation. We discuss the role of geometric invariant theory (GIT) in approaching the solvability of the dHYM equation, following work of the first author and S.-T. Yau. We compare the GIT picture with the conjectural picture for dHYM involving Bridgeland stability. In particular, following Arcara-Miles, we show that on the blow-up of $\mathbb{P}^2$ any line bundle admitting a solution of the deformed Hermitian-Yang-Mills equation is Bridgeland stable, but not conversely. Finally, we survey some recent progress on heat flows associated to the dHYM equation.
