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Nakayama Lab
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The lab studies the birational geometry of algebraic varieties and complex manifolds.
AboutAbout the lab
Studying the structure of varieties through invariants.
The Nakayama Lab studies the birational geometry of algebraic varieties and complex manifolds.
Using birational invariants such as the Kodaira dimension and plurigenera, the lab investigates the structure of varieties, placing particular emphasis on invariants related to the canonical divisor.
The lab has also long worked on the classification of varieties that admit surjective endomorphisms that are not isomorphisms, and on ℚ-Gorenstein deformations.
Key terms
- Birational geometry
- A branch of geometry that treats varieties that can be regarded as having the same shape, apart from some portion, as the same, and studies their structure
- Kodaira dimension
- One of the birational invariants determined by the canonical divisor. It serves as a key clue for the broad classification of varieties
- Endomorphism (self-holomorphic map)
- A holomorphic (complex-analytic or algebraic) map from a variety to itself
ResearchResearch themes
The lab studies the birational geometry of algebraic varieties and complex manifolds. It is interested in birational invariants related to the canonical divisor and in the concrete structure of varieties thought to be important in birational geometry, and it also works on the classification of varieties with endomorphisms and on ℚ-Gorenstein deformations.
*Illustrative imageBirational Invariants and the Structure of Varieties
Interested in invariants and the concrete structure of varieties, the lab has studied numerical properties of divisors, such as the Zariski decomposition, and the structure of elliptic fibrations.
*Illustrative imageClassification of Varieties with Endomorphisms
The lab has long worked, including through joint research, on classifying varieties that admit surjective endomorphisms that are not isomorphisms. It has obtained notable results on the classification for normal projective algebraic surfaces.
*Illustrative imageℚ-Gorenstein Deformations
Through joint research, the lab extended to positive characteristic the method of Lee-Park, which constructs simply connected surfaces of general type with genus zero by ℚ-Gorenstein deformations of special singular rational surfaces.
MembersFaculty
- Associate ProfessorNoboru Nakayama
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: “Sarti dodectic 360” Salix alba / CC BY-SA 4.0 (cropped)
- Birational Invariants and the Structure of Varieties: “Sarti sextic 48 A” Salix alba / CC BY-SA 4.0 (cropped)
- Classification of Varieties with Endomorphisms: “Fatou sets for Blaschke fraction f(z) = rho * z^2 * (z-3) over (1-3z)” Adam majewski / CC BY-SA 4.0 (cropped)
- ℚ-Gorenstein Deformations: “Sarti sextic 48 (Stabchen)” Salix alba / CC BY-SA 4.0 (cropped)
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