Hartshorne Algebraic Geometry
E883474
Hartshorne Algebraic Geometry is a foundational graduate-level textbook by Robin Hartshorne that systematically develops modern algebraic geometry using schemes and cohomology.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Hartshorne Algebraic Geometry canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10732823 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Hartshorne Algebraic Geometry Context triple: [Serre duality, appearsIn, Hartshorne Algebraic Geometry]
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A.
Eisenbud’s Commutative Algebra
Eisenbud’s *Commutative Algebra* is a widely used graduate-level textbook that develops modern commutative algebra with strong connections to algebraic geometry, featuring topics such as free resolutions, syzygies, and Castelnuovo–Mumford regularity.
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B.
Foundations of Algebraic Geometry
Foundations of Algebraic Geometry is a landmark mathematical treatise that systematically developed the modern foundations of algebraic geometry and profoundly influenced the field’s subsequent evolution.
-
C.
Chevalley’s theorem in algebraic geometry
Chevalley’s theorem in algebraic geometry is a fundamental result stating that the image of a morphism of finite type between schemes (or varieties) is a constructible set, playing a key role in understanding how geometric properties behave under mappings.
-
D.
Topological Methods in Algebraic Geometry
Topological Methods in Algebraic Geometry is a foundational mathematical monograph by Friedrich Hirzebruch that applies topological techniques, particularly characteristic classes and cobordism theory, to problems in algebraic geometry.
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E.
Lazarsfeld’s Positivity in Algebraic Geometry
Lazarsfeld’s *Positivity in Algebraic Geometry* is a two-volume monograph that serves as a standard modern reference on the theory of positivity for line bundles and divisors in algebraic geometry, integrating techniques from cohomology, vanishing theorems, and birational geometry.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Hartshorne Algebraic Geometry Target entity description: Hartshorne Algebraic Geometry is a foundational graduate-level textbook by Robin Hartshorne that systematically develops modern algebraic geometry using schemes and cohomology.
-
A.
Eisenbud’s Commutative Algebra
Eisenbud’s *Commutative Algebra* is a widely used graduate-level textbook that develops modern commutative algebra with strong connections to algebraic geometry, featuring topics such as free resolutions, syzygies, and Castelnuovo–Mumford regularity.
-
B.
Foundations of Algebraic Geometry
Foundations of Algebraic Geometry is a landmark mathematical treatise that systematically developed the modern foundations of algebraic geometry and profoundly influenced the field’s subsequent evolution.
-
C.
Chevalley’s theorem in algebraic geometry
Chevalley’s theorem in algebraic geometry is a fundamental result stating that the image of a morphism of finite type between schemes (or varieties) is a constructible set, playing a key role in understanding how geometric properties behave under mappings.
-
D.
Topological Methods in Algebraic Geometry
Topological Methods in Algebraic Geometry is a foundational mathematical monograph by Friedrich Hirzebruch that applies topological techniques, particularly characteristic classes and cobordism theory, to problems in algebraic geometry.
-
E.
Lazarsfeld’s Positivity in Algebraic Geometry
Lazarsfeld’s *Positivity in Algebraic Geometry* is a two-volume monograph that serves as a standard modern reference on the theory of positivity for line bundles and divisors in algebraic geometry, integrating techniques from cohomology, vanishing theorems, and birational geometry.
- F. None of above. chosen
Statements (53)
| Predicate | Object |
|---|---|
| instanceOf |
algebraic geometry textbook
ⓘ
mathematics book ⓘ textbook ⓘ |
| author | Robin Hartshorne NERFINISHED ⓘ |
| countryOfPublication |
United States of America
ⓘ
surface form:
United States
|
| field | algebraic geometry ⓘ |
| hasPart |
Chapter I: Varieties
ⓘ
Chapter II: Schemes ⓘ Chapter III: Cohomology NERFINISHED ⓘ Chapter IV: Varieties of Dimension 1 ⓘ Chapter V: Curves NERFINISHED ⓘ |
| influenced | modern scheme-theoretic approach to algebraic geometry ⓘ |
| language | English ⓘ |
| level | graduate ⓘ |
| publicationYear | 1977 ⓘ |
| publisher | Springer-Verlag NERFINISHED ⓘ |
| series | Graduate Texts in Mathematics NERFINISHED ⓘ |
| subject |
Castelnuovo–Mumford regularity
NERFINISHED
ⓘ
Chow groups ⓘ Ext functor ⓘ Hilbert polynomial ⓘ Noetherian schemes ⓘ Picard group ⓘ Riemann–Roch theorem NERFINISHED ⓘ Serre duality NERFINISHED ⓘ Tor functor ⓘ Zariski topology NERFINISHED ⓘ affine schemes ⓘ birational geometry ⓘ blow-ups ⓘ coherent sheaves ⓘ cohomology of projective space ⓘ derived functors ⓘ dimension theory ⓘ divisors ⓘ duality theory ⓘ flat morphisms ⓘ intersection theory ⓘ line bundles ⓘ normal varieties ⓘ projective schemes ⓘ proper morphisms ⓘ quasi-coherent sheaves ⓘ rational maps ⓘ schemes ⓘ separated schemes ⓘ sheaf cohomology ⓘ singularities ⓘ smooth morphisms ⓘ varieties ⓘ étale morphisms ⓘ |
| usedAs | standard reference in algebraic geometry ⓘ |
| volumeNumberInSeries | 52 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Hartshorne Algebraic Geometry Description of subject: Hartshorne Algebraic Geometry is a foundational graduate-level textbook by Robin Hartshorne that systematically develops modern algebraic geometry using schemes and cohomology.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.