arXiv subjects

Meeyoung Kim

Publications and source records attributed to Meeyoung Kim.

3 recordsLinked to original sources

arXiv2001

Theorems of Barth-Lefschetz type on Kaehler manifolds of non-negative bisectional curvature

Theorems of Barth-Lefschetz type describe restrictions on the topology of varieties of small codimension. R. Schoen and J. Wolfson, using Morse theory on a path space, have described a technique to prove theorems of this kind for complex submanifolds of Kähler manifolds of non-negative holomorphic bisectional curvature. In this paper this program is carried out for the compact Hermitian symmetric spaces. The key technical point is to define and compute an invariant, called the {\it complex positivity}, that measures the ``amount'' of positive curvature, in a suitable sense.

math.AG↗

arXiv1999

Zero Assignment, Pole Placement and Matrix Extension Problems: A Common Point of View

The paper studies a general inverse eigenvalue problem which contains as special cases many well studied pole placement and matrix extension problems. It is shown that the studied problem corresponds on the geometric side to a central projection from some projective variety. The degree for this variety is computed in the critical dimension.

math.OC↗

arXiv1998

On branched coverings of some homogeneous spaces

We study nonsingular branched coverings of a homogeneous space X. There is a vector bundle associated with such a covering which was conjectured by O. Debarre to be ample when the Picard number of X is one. We prove this conjecture, which implies Barth-Lefschetz type theorems, for lagrangian grassmannians, and for quadrics up to dimension six. We propose a conjectural extension to homogeneous spaces of Picard number larger than one and prove a weaker version.

math.AG↗