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Koike Lab
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A complex geometry lab that studies metrics on line bundles over complex manifolds.
AboutAbout the lab
Exploring metrics on line bundles and complex geometry
The Koike Lab studies complex geometry and the theory of functions of several complex variables.
Among Hermitian metrics on line bundles over complex manifolds, the lab is interested in those with singularities, and especially those with the mildest singularities.
The lab is also interested in the complex analytic geometry of neighborhoods of compact submanifolds (such as Ueda theory) and its applications.
Key terms
- Complex manifold
- A space in which the neighborhood of each point can be described with complex coordinates. It is the main object of study in complex geometry
- Line bundle
- A structure that attaches a one-dimensional complex space (a single complex number's worth of extent) to each point of a space
- Hermitian metric
- A rule that measures the length of vectors at each point of a line bundle
- Ueda theory
- One of the theories used to study the complex analytic geometry of neighborhoods of compact submanifolds
- Theory of functions of several complex variables
- A field of mathematics that studies functions of several complex variables
- Singular Hermitian metric
- A rule for measuring length at each point of a line bundle whose smoothness breaks down at some places
NewsLab news
A paper by Professor Koike and colleagues was published in Publications of the Research Institute for Mathematical Sciences
A paper by Professor Koike and colleagues was published in Mathematische Zeitschrift
A paper by Professor Koike and colleagues was published in Journal of Differential Geometry
ResearchResearch themes
The lab's research fields are complex geometry and the theory of functions of several complex variables. It is interested in Hermitian metrics on line bundles over complex manifolds and in the complex analytic geometry of neighborhoods of compact submanifolds.
*Illustrative imageMinimal Singular Hermitian Metrics on Line Bundles
The lab is interested in singular Hermitian metrics on line bundles over complex (algebraic) manifolds. It focuses in particular on metrics with semipositive curvature that have the mildest possible singularities (minimal singular metrics).
*Illustrative imageComplex Analytic Geometry of Neighborhoods of Complex Submanifolds
In connection with the flatness of topologically trivial holomorphic line bundles, the lab is also interested in the complex analytic geometry of neighborhoods of compact submanifolds, including Ueda theory, and its applications.
MembersFaculty
- ProfessorTakayuki Koike
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Complex plot for derangement function re and im between -9 to 9” A2569875 / CC BY-SA 4.0 (cropped)
- Minimal Singular Hermitian Metrics on Line Bundles: “Willmore Surface sculpture Durham” Chemical Engineer / CC BY-SA 4.0 (cropped)
- Complex Analytic Geometry of Neighborhoods of Complex Submanifolds: “Calabi-Yau” Lunch / CC BY-SA 2.5 (cropped)
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