Lazarsfeld’s Positivity in Algebraic Geometry
E790525
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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Lazarsfeld’s Positivity in Algebraic Geometry canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T9297118 — 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: Lazarsfeld’s Positivity in Algebraic Geometry Context triple: [Castelnuovo–Mumford regularity, studiedIn, Lazarsfeld’s Positivity in Algebraic Geometry]
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A.
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.
-
B.
Hodge–Riemann bilinear relations
The Hodge–Riemann bilinear relations are fundamental positivity and orthogonality conditions on the intersection form in Hodge theory that underpin results such as the hard Lefschetz theorem and the Hodge index theorem.
-
C.
Standard Conjectures on Algebraic Cycles
The Standard Conjectures on Algebraic Cycles are a set of deep, still unproven hypotheses in algebraic geometry that aim to provide a foundational theory of algebraic cycles and their cohomological properties, underpinning much of the modern theory of motives.
-
D.
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.
-
E.
Brill–Noether theory
Brill–Noether theory is a branch of algebraic geometry that studies linear series on algebraic curves, particularly the existence and dimension of spaces of special divisors and maps to projective spaces.
- 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: Lazarsfeld’s Positivity in Algebraic Geometry Target entity description: 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.
-
A.
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.
-
B.
Hodge–Riemann bilinear relations
The Hodge–Riemann bilinear relations are fundamental positivity and orthogonality conditions on the intersection form in Hodge theory that underpin results such as the hard Lefschetz theorem and the Hodge index theorem.
-
C.
Standard Conjectures on Algebraic Cycles
The Standard Conjectures on Algebraic Cycles are a set of deep, still unproven hypotheses in algebraic geometry that aim to provide a foundational theory of algebraic cycles and their cohomological properties, underpinning much of the modern theory of motives.
-
D.
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.
-
E.
Brill–Noether theory
Brill–Noether theory is a branch of algebraic geometry that studies linear series on algebraic curves, particularly the existence and dimension of spaces of special divisors and maps to projective spaces.
- F. None of above. chosen
Statements (42)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematics monograph ⓘ |
| audience |
graduate students in mathematics
ⓘ
researchers in algebraic geometry ⓘ |
| author |
Robert Lazarsfeld
NERFINISHED
ⓘ
Robert Lazarsfeld NERFINISHED ⓘ Robert Lazarsfeld NERFINISHED ⓘ |
| field | algebraic geometry ⓘ |
| focus |
theory of positivity for divisors
ⓘ
theory of positivity for line bundles ⓘ |
| format | two-volume work ⓘ |
| language | English ⓘ |
| status | standard modern reference ⓘ |
| subtitle |
Classical Setting: Line Bundles and Linear Series
ⓘ
Positivity for Vector Bundles, and Multiplier Ideals NERFINISHED ⓘ |
| topic |
Castelnuovo–Mumford regularity
NERFINISHED
ⓘ
Fujita’s conjecture NERFINISHED ⓘ Kawamata–Viehweg vanishing NERFINISHED ⓘ Kodaira vanishing theorem NERFINISHED ⓘ Okounkov bodies NERFINISHED ⓘ Seshadri constants NERFINISHED ⓘ Zariski decompositions ⓘ ample line bundles ⓘ asymptotic base loci ⓘ asymptotic cohomology ⓘ base loci of linear series ⓘ birational geometry ⓘ birational invariants ⓘ cohomology of line bundles ⓘ multiplier ideals ⓘ nef line bundles ⓘ positivity of divisors ⓘ positivity of line bundles ⓘ restricted volumes ⓘ vanishing theorems ⓘ very ample line bundles ⓘ |
| usesTechnique |
birational geometry methods
ⓘ
cohomological methods ⓘ multiplier ideal techniques ⓘ vanishing theorems ⓘ |
| volume |
Positivity in Algebraic Geometry I
NERFINISHED
ⓘ
Positivity in Algebraic Geometry II NERFINISHED ⓘ |
How these facts were elicited
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Subject: Lazarsfeld’s Positivity in Algebraic Geometry Description of subject: 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.
Referenced by (1)
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