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Algebra 2 (Algebraic Geometry) Lab
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The lab studies the minimal model program in positive characteristic.

AboutAbout the lab
Classifying shapes in another world of numbers
Prof. Tanaka's lab studies the minimal model program, a classification theory for algebraic varieties, in positive characteristic.
The lab investigates the properties of Fano threefolds and del Pezzo surfaces in positive characteristic.
Key terms
- Minimal model program
- A theory that classifies algebraic varieties by transforming them into their simplest form (minimal models)
- Positive characteristic
- A world of numbers, like finite fields, in which adding 1 to itself a prime number p of times gives 0
- Fano threefold
- A three-dimensional algebraic variety that curves consistently in the positive direction. It is a basic building block of classification
ResearchResearch themes
The lab studies the minimal model program, a classification theory for algebraic varieties, in positive characteristic.
View More ↗MembersFaculty
- Associate ProfessorHiromu Tanaka
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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: “Clebsch Cubic” Fly by Night / CC BY-SA 3.0 (cropped)
- Fano threefolds in positive characteristic: “Modell der Diagonalfläche von Clebsch -Schilling VII, 1 - 44” Oliver Zauzig / CC BY-SA 3.0 (cropped)
- Related lab (Algebra 2 (Algebraic Geometry) Lab (Osamu Fujino)): “Sarti's octic with 144 nodes” Salix alba / CC BY-SA 4.0 (cropped)
- Related lab (Algebra 2 (Algebraic Geometry) Lab (Shu Kawaguchi)): “Tropical curves 3rd order” Erwan Brugallé, Ilia Itenberg, Kristin Shaw, Oleg Viro / CC BY-SA 4.0 (cropped)
- Related lab (Algebra 2 and Geometry 2 Lab (Complex Geometry, Algebraic Geometry, Differential Geometry; Kenichi Yoshikawa)): “Espace de Calabi-Yau” Rogilbert / Public domain (cropped)
- Related lab (Analysis 2 (Operator Algebras, Functional Analysis) Lab (Masaki Izumi)): “JonesLink” ProfKnots / CC BY-SA 4.0 (cropped)
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