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Infinite Analysis Lab (Namikawa)
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The lab studies Calabi-Yau varieties and symplectic varieties with singularities.
AboutAbout the lab
Exploring singular spaces through deformation theory and birational geometry
The Namikawa Lab studies, in the field of algebraic geometry, algebraic varieties whose canonical bundle is trivial.
Its subjects are compact Calabi-Yau varieties, hyperkähler varieties, and non-compact algebraic varieties with a complex symplectic structure.
The lab investigates such varieties with singularities from the viewpoints of birational geometry, deformation theory, and singularity theory.
Key terms
- Algebraic variety
- A geometric object represented as the set of solutions of polynomial equations, and the main object of study in algebraic geometry
- Singularity
- A point where a geometric object is not smooth, for example because it has a sharp point or self-intersection
- Calabi-Yau variety
- A compact algebraic variety with trivial canonical bundle, an important object in classification theory and mirror symmetry
- Poisson deformation
- An approach that studies non-compact conical symplectic singularities by deforming them together with their Poisson structure
ResearchResearch themes
The lab studies algebraic varieties with trivial canonical bundle that have singularities, from the viewpoints of birational geometry, deformation theory, and singularity theory. Its research subjects fall into three groups: 3-dimensional Calabi-Yau varieties, compact complex symplectic varieties, and non-compact complex symplectic varieties.
*Illustrative image3-dimensional Calabi-Yau varieties
The lab proved that a 3-dimensional Calabi-Yau variety with Q-factorial terminal singularities can be deformed to a nonsingular Calabi-Yau variety.
*Illustrative imageCompact complex symplectic varieties
For varieties with Q-factorial terminal singularities, the lab defined a period map and proved a local Torelli-type theorem. It also gave a counterexample to the (birational) global Torelli-type theorem, which had long been unresolved in the nonsingular case.
*Illustrative imageSymplectic singularities and Poisson deformations
The lab developed a general theory of Poisson deformations and proved that Poisson deformations of conical symplectic singularities are unobstructed. It also characterized nilpotent cones and toric hyperkähler varieties among conical symplectic singularities.
MembersFaculty
- ProfessorYoshinori Namikawa
VoicesStudent voices
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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: “Consani-Scholten” Ursulageorges / CC BY 4.0 (cropped)
- 3-dimensional Calabi-Yau varieties: “Quintic 1” The original uploader was Floriang at German Wikipedia. / CC BY-SA 3.0 (cropped)
- Compact complex symplectic varieties: “K3 surface” BTotaro / CC BY-SA 4.0 (cropped)
- Symplectic singularities and Poisson deformations: “Weyl group for A2” Mathphysman / CC BY-SA 4.0 (cropped)
- Related lab (Infinite Analysis Lab (Odaka)): “Quartic Fermat curve” Jacob Rus / CC BY-SA 4.0 (cropped)
- Related lab (Tamagawa Lab): “Klein-map” PSL27 / CC BY-SA 4.0 (cropped)
- Related lab (Infinite Analysis Lab (Mochizuki)): “Kyoto University RIMS” KATSURA Roen / CC BY 3.0 (cropped)
- Related lab (Infinite Analysis Research Division (Hoshi) Lab): “Kleinian group limit set on sphere” Adam majewski / CC BY-SA 4.0 (cropped)
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