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Takayama Lab
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A complex geometry lab that studies complex algebraic varieties using analytic methods.
AboutAbout the lab
Algebraic shapes, studied with analytic tools.
Takayama Lab studies complex algebraic varieties in the field of complex geometry, using analytic methods.
The lab applies singular Hermitian metrics on line bundles, multiplier ideal sheaves, and Kodaira-type cohomology vanishing theorems to investigate the algebraic and geometric properties of varieties.
Recently, the lab has been particularly interested in Hodge metrics associated with pluricanonical bundles and their relative versions.
Key terms
- Complex algebraic variety
- A geometric object defined as the zero set of polynomials with complex coefficients
- Line bundle
- A construction that attaches a one-dimensional line smoothly to each point of a geometric object
- Multiplier ideal sheaf
- A tool for recording the singularities of a metric (how it diverges) in algebraic form
ResearchResearch themes
The lab's research field is complex geometry, with pluricanonical bundles and multiplier ideal sheaves as its themes. It investigates the properties of complex algebraic varieties using analytic methods.
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MembersFaculty
- ProfessorShigeharu TakayamaPublications ↗
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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: “Togliatti surface” Claudio Rocchini / CC BY-SA 3.0 (cropped)
- Pluricanonical Bundles and Multiplier Ideal Sheaves: “K3 surface” BTotaro / CC BY-SA 4.0 (cropped)
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