Datar Ved, Jacob Adam
Department of Mathematics, Indian Institute of Science, Bengaluru, India.
Department of Mathematics, UC Davis, One Shields Ave, Davis, CA USA.
J Geom Anal. 2022;32(2):69. doi: 10.1007/s12220-021-00808-9. Epub 2022 Jan 7.
Let be an elliptically fibered 3 surface, admitting a sequence of Ricci-flat metrics collapsing the fibers. Let be a holomorphic () bundle over , stable with respect to . Given the corresponding sequence of Hermitian-Yang-Mills connections on , we prove that, if is a generic fiber, the restricted sequence converges to a flat connection . Furthermore, if the restriction is of the form for distinct points , then these points uniquely determine .
设(X)是一个椭圆纤维化的三维曲面，它允许一列Ricci - 平坦度量使纤维坍缩。设(E)是(X)上的一个全纯((\mathbb{C}))丛，关于某个极化是稳定的。给定(E)上相应的一列Hermitian - Yang - Mills联络，我们证明，如果(F)是一个一般纤维，那么限制序列收敛到一个平坦联络。此外，如果限制(A_{|F})具有(\sum_{i = 1}^{n}a_{i}\delta_{p_{i}})的形式，其中(p_{i})是不同的点，那么这些点唯一地确定(A)。
