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Gongyo Lab
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The lab classifies higher-dimensional algebraic varieties by focusing on their canonical divisors.
AboutAbout the lab
Classifying higher-dimensional algebraic varieties
The Gongyo Lab studies geometry in the field of algebraic geometry, focusing on the canonical divisors of algebraic varieties.
In particular, it studies the abundance conjecture, one of the most important conjectures in higher-dimensional algebraic geometry.
The lab has also studied (semi-)log canonical pairs, the canonical bundle formula, the subadjunction formula, log Fano varieties, and applications of techniques for reduction to positive characteristic.
Key terms
- Algebraic variety
- A geometric object formed as the set of solutions to polynomial equations
- Canonical divisor
- A quantity naturally attached to an algebraic variety that strongly reflects properties of the variety's shape
- Abundance conjecture
- The conjecture that, for a minimal model, a sufficiently large multiple of the canonical divisor defines a well-behaved map
ResearchResearch themes
The lab's research theme is the classification of higher-dimensional algebraic varieties, studying geometry that focuses on the canonical divisors of algebraic varieties. In particular, it works on the abundance conjecture.
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MembersFaculty
- ProfessorYoshinori GongyoPublications ↗
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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: “Mathematisches-Gipsmodell.Fläche3.Ordnung - Kopie” Museopedia / CC BY-SA 4.0 (cropped)
- Classification of Higher-Dimensional Algebraic Varieties: “Clebsch Cubic” Fly by Night / CC BY-SA 3.0 (cropped)
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- 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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