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Takagi Lab
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A commutative algebra and algebraic geometry lab that studies singularities using the Frobenius morphism.
AboutAbout the lab
Studying the sharp points of shapes in positive characteristic
Takagi Lab studies singularities of algebraic varieties from the perspectives of commutative algebra and algebraic geometry.
The lab studies F-singularities, which are singularities in positive characteristic defined using the Frobenius morphism.
As an application, the lab is also interested in the properties of singularities that appear in the minimal model program, and in the geometric properties of Frobenius split varieties.
Key terms
- singularity
- A point where a shape is not smooth, such as a sharp point or a place where the shape crosses itself
- algebraic variety
- A shape described as the set of solutions of polynomial equations
- Frobenius morphism
- A map specific to positive characteristic, built from the map that raises numbers to the p-th power
ResearchResearch themes
The lab studies singularities of algebraic varieties. It works on F-singularities in positive characteristic, which are defined using the Frobenius morphism, and on their applications to the minimal model program and Frobenius split varieties.
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MembersFaculty
- ProfessorShunsuke TakagiPublications ↗
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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: “CayleyCubic” Salix alba / CC BY-SA 3.0 (cropped)
- Singularities of Algebraic Varieties: “Surface of degree 7” Jean Constant / CC BY-SA 4.0 (cropped)
- Related lab (Ito Lab): “Tetrahedroid” Salix alba / CC BY-SA 4.0 (cropped)
- Related lab (Oguiso Lab): “Calabi yau” Jbourjai / Public domain (cropped)
- Related lab (Kawakami Lab): “BarthSextic” Mike Williams / Public domain (cropped)
- Related lab (Kelly Lab): “Spectral Sequence Visualization” L.penguu / CC BY-SA 4.0 (cropped)
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